[Turtle]

sigurdV, on 28 January 2012 - 03:21 PM, said:

Hi There Friendly Turtle!

...
Isnt?: Is this one? = Is "Is this one?" one?
Then isnt? : Is this one? + Is this one? = Is this one?

PS2
# 903 is exciting for us interested non mathematicians
(Sneaks out, on tip toe, inside this thread them wizards work...Hush!)

PS3 Found this turtle quote:
___The very fundamental axiom of probability is false. i.e. 'assume equal probability', Otherwise called 'fairness', there is no such thing.

Are you choosing the correct wording here?
axiom = assumption, surely?

sorry, i have no interest in which 1, what 1, or anyone.
glad the summary was helpful.
i wrote that quote in a delusional fit; you probably shouldn't put any stock in it.

phillip1882, on 31 January 2012 - 08:43 PM, said:

mumble grumble.... I'll get there.

the primes are a bit more of a challenge, not so much because it's difficult to sieve them out, though it is, but because i would have to do it at the same time as I'm sieving out the figurates.

roger. are you sure you didn't keep the original code? props for your cahones rewriting these from scratch.

i finished my runs and have 1000 files of tallies going to 1000000000. 71 gigs.

the thing is, i don't like the final total as i get it at 10 more than donk's density calc & i think it should be 5 less. better check me as i used a calculator again.

here's donk's result and the last few entries of the last file.

donk: >> 1,000,000,000 : 640,349,984 359,650,016 50,847,531 308,802,485

turtle: >> m_densities999.txt
999999987 1 385372855 177756202 56853573 15170769 3854989 990078 257476 68450 18444 5097 1413 436 141 29 12 5 1 0 0 0 0
999999988 2 385372855 177756203 56853573 15170769 3854989 990078 257476 68450 18444 5097 1413 436 141 29 12 5 1 0 0 0 0
999999990 1 385372856 177756203 56853573 15170769 3854989 990078 257476 68450 18444 5097 1413 436 141 29 12 5 1 0 0 0 0
999999991 1 385372857 177756203 56853573 15170769 3854989 990078 257476 68450 18444 5097 1413 436 141 29 12 5 1 0 0 0 0
999999993 2 385372857 177756204 56853573 15170769 3854989 990078 257476 68450 18444 5097 1413 436 141 29 12 5 1 0 0 0 0
999999994 2 385372857 177756205 56853573 15170769 3854989 990078 257476 68450 18444 5097 1413 436 141 29 12 5 1 0 0 0 0
999999995 1 385372858 177756205 56853573 15170769 3854989 990078 257476 68450 18444 5097 1413 436 141 29 12 5 1 0 0 0 0
999999996 2 385372858 177756206 56853573 15170769 3854989 990078 257476 68450 18444 5097 1413 436 141 29 12 5 1 0 0 0 0
999999999 1 385372859 177756206 56853573 15170769 3854989 990078 257476 68450 18444 5097 1413 436 141 29 12 5 1 0 0 0 0
1000000000 3 385372859 177756206 56853574 15170769 3854989 990078 257476 68450 18444 5097 1413 436 141 29 12 5 1 0 0 0 0

[phillip1882]

385372859 
177756206 563129065
 56853574 619982639
 15170769 635153408
  3854989 639008397
   990078 639998475
   257476 640255951
    68450 640324401
    18444 640342845
     5097 640347942
     1413 640349355
      436 640349791
      141 640349932
       29 640349961
       12 640349973
        5 640349978
+       1 640349979

640,349,984 -5 = 64039979

[Turtle]

phillip1882, on 03 February 2012 - 06:10 PM, said:

385372859 
177756206 563129065
 56853574 619982639
 15170769 635153408
  3854989 639008397
   990078 639998475
   257476 640255951
    68450 640324401
    18444 640342845
     5097 640347942
     1413 640349355
      436 640349791
      141 640349932
       29 640349961
       12 640349973
        5 640349978
+       1 640349979

640,349,984 -5 = 64039979

mmmm...i can't add (or subtract?) & you can't type.

640,349,984 -5 = 640349979

while you bash out the primes, , i'm going to start making another 1000 files but with the [n, s] results as we did originally. i have something similar in mind for the non-poly prog once it's ready.

[Turtle]

finished the new set of 1000 files for all polys from 6 to 1000000000 with their multiplicities. only 20.5 gigs. following up on the previous set, i pulled out all the first m's to m17. here's those.

first m's:
1: 6 1 [3, 3]
2: 15 2 [3, 6, 5, 3]
3: 36 3 [3, 13, 6, 4, 8, 3]
4: 225 4 [3, 76, 5, 24, 9, 8, 15, 4]
5: 561 5 [3, 188, 6, 39, 11, 12, 17, 6, 33, 3]
6: 1225 6 [5, 124, 7, 60, 10, 29, 25, 6, 35, 4, 49, 3]
7: 11935 7 [5, 1195, 7, 570, 10, 267, 14, 133, 35, 22, 55, 10, 154, 3]
8: 11781 8 [3, 3928, 6, 787, 9, 329, 11, 216, 21, 58, 63, 8, 77, 6, 153, 3]
9: 27405 9 [3, 9136, 5, 2742, 9, 763, 14, 303, 18, 181, 27, 80, 35, 48, 63, 16, 105, 7]
10: 220780 10 [4, 36798, 7, 10515, 10, 4908, 14, 2428, 19, 1293, 28, 586, 35, 373, 38, 316, 40, 285, 664, 3]
11: 203841 11 [3, 67948, 6, 13591, 9, 5664, 11, 3708, 29, 504, 33, 388, 66, 97, 71, 84, 99, 44, 261, 8, 638, 3]
12: 3368925 12 [3, 1122976, 5, 336894, 9, 93583, 14, 37023, 18, 22021, 27, 9600, 35, 5664, 69, 1438, 75, 1216, 105, 619, 207, 160, 630, 19]
13: 4921840 13 [4, 820308, 7, 234375, 10, 109376, 14, 54088, 32, 9925, 40, 6312, 47, 4555, 70, 2040, 94, 1128, 119, 703, 187, 285, 235, 181, 280, 128]
14: 7316001 14 [3, 2438668, 6, 487735, 9, 203224, 11, 133020, 17, 53796, 21, 34840, 33, 13858, 51, 5740, 63, 3748, 81, 2260, 119, 1044, 126, 931, 161, 570, 621, 40]
15: 33631521 15 [3, 11210508, 6, 2242103, 11, 611484, 14, 369579, 21, 160152, 33, 63698, 41, 41016, 53, 24408, 66, 15681, 77, 11496, 231, 1268, 371, 492, 737, 126, 1407, 36, 1749, 24]
16: 142629201 16 [3, 47543068, 6, 9508615, 9, 3961924, 11, 2593260, 17, 1048746, 26, 438861, 33, 270133, 39, 192484, 41, 173940, 51, 111868, 99, 29404, 153, 12268, 246, 4735, 351, 2324, 533, 1008, 561, 910]
17: 879207616 17 [4, 146534604, 7, 41867031, 14, 9661624, 16, 7326732, 28, 2325948, 31, 1890771, 56, 570916, 58, 531888, 118, 127368, 236, 31708, 248, 28708, 406, 10696, 496, 7164, 518, 6568, 1711, 603, 2146, 384, 7192, 36]

[phillip1882]

still hammering away. i should have something presentable by sunday. i hope.

[Turtle]

phillip1882, on 09 February 2012 - 07:37 PM, said:

still hammering away. i should have something presentable by sunday. i hope.

oh thank monsters!!! i ran another 100,000,000 on the tally prog just to stay productive. 80 gigs and counting. help me obie wan kaphilly!

m_densities1099 said:

1099999978 2 423909821 195531573 62539926 16688270 4240315 1089079 283234 75325 20273 5645 1549 471 156 32 12 5 1 0 0 0 0 0 0 0
1099999980 2 423909821 195531574 62539926 16688270 4240315 1089079 283234 75325 20273 5645 1549 471 156 32 12 5 1 0 0 0 0 0 0 0
1099999983 1 423909822 195531574 62539926 16688270 4240315 1089079 283234 75325 20273 5645 1549 471 156 32 12 5 1 0 0 0 0 0 0 0
1099999984 1 423909823 195531574 62539926 16688270 4240315 1089079 283234 75325 20273 5645 1549 471 156 32 12 5 1 0 0 0 0 0 0 0
1099999985 1 423909824 195531574 62539926 16688270 4240315 1089079 283234 75325 20273 5645 1549 471 156 32 12 5 1 0 0 0 0 0 0 0
1099999986 3 423909824 195531574 62539927 16688270 4240315 1089079 283234 75325 20273 5645 1549 471 156 32 12 5 1 0 0 0 0 0 0 0
1099999989 3 423909824 195531574 62539928 16688270 4240315 1089079 283234 75325 20273 5645 1549 471 156 32 12 5 1 0 0 0 0 0 0 0
1099999990 2 423909824 195531575 62539928 16688270 4240315 1089079 283234 75325 20273 5645 1549 471 156 32 12 5 1 0 0 0 0 0 0 0
1099999992 1 423909825 195531575 62539928 16688270 4240315 1089079 283234 75325 20273 5645 1549 471 156 32 12 5 1 0 0 0 0 0 0 0
1099999995 2 423909825 195531576 62539928 16688270 4240315 1089079 283234 75325 20273 5645 1549 471 156 32 12 5 1 0 0 0 0 0 0 0
1099999996 1 423909826 195531576 62539928 16688270 4240315 1089079 283234 75325 20273 5645 1549 471 156 32 12 5 1 0 0 0 0 0 0 0
1099999998 1 423909827 195531576 62539928 16688270 4240315 1089079 283234 75325 20273 5645 1549 471 156 32 12 5 1 0 0 0 0 0 0 0
1099999999 1 423909828 195531576 62539928 16688270 4240315 1089079 283234 75325 20273 5645 1549 471 156 32 12 5 1 0 0 0 0 0 0 0
1100000000 1 423909829 195531576 62539928 16688270 4240315 1089079 283234 75325 20273 5645 1549 471 156 32 12 5 1 0 0 0 0 0 0 0

[Turtle]

hey phillip (et al). so i was poking around the python tutorial trying to get some sense for what it has in the way of drawing capabilities that i/we might apply to our graphing pursuits. anyway, i found they have a turtle module (how appropriate, eh? ) and on the face of it it sounds ideal for making my spiral arrays. are you aware of it or have you ever worked with it? it's beyond my grasp so far -and maybe my reach too- but thought i'd bring it to an expert's attention. here's the link; let me know what you think. no hurry or need to drop what you're doing.

Turtle graphics for Tk

[Turtle]

in the intermission, more musings and some eye-candy. i'm thinking to use the text files we generate as the source data for the turtle. this way we don't have to do all the "finding" on the fly and we can generate multiple views of spiral arrays by changing the color scheme. voila!! no more of my by-hand colorings as i did to get your [phillip] suggested bitwise view from your class view of the polygonal/non-polygonal spiral array of natural numbers.

polygonal/non-polygonal bitwise spiral array

[Turtle]

provided the above idea is workable and looking at the wide range of turtle options, we may now be able to write a program to generate my hand-drawn triangular spiral array of natural numbers with any coloring we choose.

[phillip1882]

okay it's official; turtle has no life beyond math!

here' my current attempt. please note there are most likely errors; i didn't spot any quick and ready ones, but I'm almost positive they are there.
(side note; i didn't leave out the trivial non-figs, although it wouldn't be hard to do so; if you really care I'll put that code in turtle.)

max = 10000000
current = 1000000
increment = 1000000
figs = [False]*increment
primes = [True]*increment
x = 2
row = 6
col = 3
inc = 3
colinc = 3
name = "poly"
fnum = 0
file = open(str(name)+str(fnum)+".txt","w")
while current <= max:
   if row > current-increment:
      value = row
   else:
      value = current-increment-(current-increment-row)%col+col
   while value-(current-increment)<increment:
      figs[value-(current-increment)] = True
      value += col
   if x > current-increment:
      value = x-(current-increment)+x
   else:
      value = x-(current-increment)%x +current-increment
   while value-(current-increment)<increment:
      primes[value-(current-increment)] = False
      value += x
   if x == 2:
      x += 1
   else:
      x += 2
   col = row
   inc += 1
   row += inc
   if row >current:
      soloOdd = False
      soloEven = False
      pair = False
      twin = False
      pos = current -increment
      for i in range(0, increment):
         if primes[i]:
            if twin:
               file.write(str(i-3+pos) +" " +str(i-1+pos) +" twin\n")
               twin = False
            if pair:
               file.write(str(i-3+pos) +" " +str(i-2+pos) +" pair\n")
               pair = False
            if soloEven or soloOdd:
               if figs[i-1] == True:
                  if soloEven:
                     file.write(str(i-2+pos) +" solo even\n")
                     soloEven = False
                  else:
                     file.write(str(i-2+pos) +" solo odd\n")
                     soloOdd = False
            file.write(str(i+pos) +" prime\n")
         elif figs[i] == False:
            if twin:
               file.write(str(i-3+pos)+" " +str(i-1+pos)+" " +str(i+pos) +" triple\n")
               twin = False
            elif pair:
               file.write(str(i-3+pos)+" " +str(i-2+pos)+" " +str(i+pos) +" triple\n")
               pair = False
            elif soloOdd or soloEven:
               if figs[i-1] == False:
                  pair = True
               else:
                  twin = True
               soloEven = False
               soloOdd = False
            elif i%2 == 0:
                soloEven = True
            else:
                soloOdd = True
         elif figs[i]:
            if soloEven or soloOdd:
               if figs[i-1] == True:
                  if soloEven:
                     file.write(str(i-2+pos) +" solo even\n")
                     soloEven = False
                  else:
                     file.write(str(i-2+pos) +" solo odd\n")
                     soloOdd = False
            elif pair and figs[i-1] == True:
               file.write(str(i-3+pos)+" " +str(i-2+pos)+" pair\n")
               pair = False
            elif twin:
               file.write(str(i-3+pos)+" "+str(i-1+pos) +" twin\n")
               twin = False
      print(current)
      file.close()
      fnum += 1
      file = open(str(name)+str(fnum)+".txt","w")
      row= 6
      col = 3
      inc = 3
      x = 2
      current += increment
      figs = [False]*increment
      primes = [True]*increment

[Turtle]

phillip1882, on 13 February 2012 - 08:46 PM, said:

okay it's official; turtle has no life beyond math!

i'll have you know that yesterday i went walkabout & romped in the un-trailed woots looking for flowers. 'course what i found was fungus, but that's beyond the point.

phillip1882 said:

here' my current attempt. please note there are most likely errors; i didn't spot any quick and ready ones, but I'm almost positive they are there.
(side note; i didn't leave out the trivial non-figs, although it wouldn't be hard to do so; if you really care I'll put that code in turtle.)

snip...

: i'll plug it in and hook it to the ol' dynometer. i'd say go ahead and do the bit to axe 1 through 6. it would be technically correct after all.

headed in........ . . . .......... . .. . .. .

[Turtle]

ok. program worked first try. comparing to old lists and seeing good data so far. first tweak needed though is for pairs. when reaching the first pair, 187, 188, they are both being written to the same line. (actually my first tweak was to rename the output file non_poly" )

non_poly0 said:

...
173 prime
179 prime
181 prime
182 solo even
187 188 pair
191 prime
193 prime
194 solo even
...

if we end up using these files to get input data this will foul the works. should be made to read:
...
173 prime
179 prime
181 prime
182 solo even
187 pair
188 pair
191 prime
193 prime
194 solo even
...

i'll go check first occurences of triplets and twins.............

[Turtle]

Turtle, on 13 February 2012 - 09:26 PM, said:

...
i'll go check first occurences of triplets and twins.............

same problem with first twins and triplet:

non_poly0 said:

...
1147 1148 pair
1151 prime
1153 prime
1154 solo even
1157 1159 twin
1163 prime
1169 solo odd
1171 prime
...

should read:
1147 1148 pair
1151 prime
1153 prime
1154 solo even
1157 twin
1159 twin
1163 prime
1169 solo odd
1171 prime
...

non_poly0 said:

...
1253 solo odd
1256 solo even
1259 prime
1262 solo even
1253 solo odd
1256 solo even
1259 prime
1262 solo even
1271 1273 1274 triple
1277 prime
1279 prime
1280 solo even
1283 prime
1286 solo even
1289 prime
1291 prime
1271 1273 1274 triple
1277 prime
1279 prime
1280 solo even
1283 prime
1286 solo even
1289 prime
1291 prime
...

should read:
...
1253 solo odd
1256 solo even
1259 prime
1262 solo even
1271 triple
1273 triple
1274 triple
1277 prime
1279 prime
1280 solo even
1283 prime
1286 solo even
1289 prime
1291 prime
...

looking correct otherwise.

edit: maybe change this:

if twin:
   file.write(str(i-3+pos) +" " +str(i-1+pos) +" twin\n")
   twin = False

to this?:

if twin:
  file.write(str(i-3+pos) +" " + " twin\n")
  file.write(str(i-1+pos) +" " + " twin\n")
  twin = False

edit:edit: nah; that didn't work.

[Turtle]

i tried several fixes but nothing worked. no matter for now because formatting aside the data looks clean. i reset max=1000000000 and jammed the throttle with a broomstick.

already saw some intersting features in non_poly5.txt.

a twin, pair, triple, triple conjunction:
5076299 5076301 twin
5076307 5076308 pair
5076311 5076313 5076314 triple
5076317 5076319 5076320 triple

a pair, pair, pair, triple:
5077531 5077532 pair
5077537 5077538 pair
5077543 5077544 pair
5077547 5077549 5077550 triple

a pair, pair, triple, triple:
5079541 5079542 pair
5079547 5079548 pair
5079551 5079553 5079554 triple
5079557 5079559 5079560 triple

thought i saw a triple triple, but can't find it now. files are taking 1 min each and they are ~5mb. yeeeeeee hawwwww! we be livin' now.

edit: aha!! triple triple in non_poly31.txt.
31985099 31985101 31985102 triple
31985111 31985113 31985114 triple
31985117 31985119 31985120 triple

[phillip1882]

alright turtle, made the necessary adjustments. I'm cheating a little for the first 6 trivial nonpolys; for the purpose of this program i declared them not prime and polygonal. (yeah it's hackish, but works.)

max = 10000000
current = 1000000
increment = 1000000
figs = [True]*6 +[False]*(increment-6)
primes = [False]*6 +[True]*(increment-6)
x = 2
row = 6
col = 3
inc = 3
colinc = 3
name = "poly"
fnum = 0
file = open(str(name)+str(fnum)+".txt","w")
while current <= max:
   if row > current-increment:
      value = row
   else:
      value = current-increment-(current-increment-row)%col+col
   while value-(current-increment)<increment:
      figs[value-(current-increment)] = True
      value += col
   if x > current-increment:
      value = x-(current-increment)+x
   else:
      value = x-(current-increment)%x +current-increment
   while value-(current-increment)<increment:
      primes[value-(current-increment)] = False
      value += x
   if x == 2:
      x += 1
   else:
      x += 2
   col = row
   inc += 1
   row += inc
   if row >current:
      soloOdd = False
      soloEven = False
      pair = False
      twin = False
      pos = current -increment
      for i in range(0, increment):
         if primes[i]:
            if twin:
               file.write(str(i-3+pos) +" twin\n") 
               file.write(str(i-1+pos) +" twin\n")
               twin = False
            if pair:
               file.write(str(i-3+pos) +" pair\n") 
               file.write(str(i-2+pos) +" pair\n")
               pair = False
            if soloEven or soloOdd:
               if figs[i-1] == True:
                  if soloEven:
                     file.write(str(i-2+pos) +" solo even\n")
                     soloEven = False
                  else:
                     file.write(str(i-2+pos) +" solo odd\n")
                     soloOdd = False
            file.write(str(i+pos) +" prime\n")
         elif figs[i] == False:
            if twin:
               file.write(str(i-3+pos)+" triple\n") 
               file.write(str(i-1+pos) +" triple\n") 
               file.write(str(i+pos) +" triple\n")
               twin = False
            elif pair:
               file.write(str(i-3+pos)+" triple\n")
               file.write(str(i-2+pos)+" triple\n") 
               file.write(str(i+pos) +" triple\n")
               pair = False
            elif soloOdd or soloEven:
               if figs[i-1] == False:
                  pair = True
               else:
                  twin = True
               soloEven = False
               soloOdd = False
            elif i%2 == 0:
                soloEven = True
            else:
                soloOdd = True
         elif figs[i]:
            if soloEven or soloOdd:
               if figs[i-1] == True:
                  if soloEven:
                     file.write(str(i-2+pos) +" solo even\n")
                     soloEven = False
                  else:
                     file.write(str(i-2+pos) +" solo odd\n")
                     soloOdd = False
            elif pair and figs[i-1] == True:
               file.write(str(i-3+pos)+" pair\n")
               file.write(str(i-2+pos)+" pair\n")
               pair = False
            elif twin:
               file.write(str(i-3+pos)+" twin\n")
               file.write(str(i-1+pos) +" twin\n")
               twin = False
      print(current)
      file.close()
      fnum += 1
      file = open(str(name)+str(fnum)+".txt","w")
      row= 6
      col = 3
      inc = 3
      x = 2
      current += increment
      figs = [False]*increment
      primes = [True]*increment

i also added the new line for each number as requested.
hope that gets you what you want.