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Posted
Turtle is endowed with perpetual birthdays with just enough time in between to recover from the hangovers. It's a scientific mystery on a grand scale!
:D

 

I told you perpetuality was possible :eek2:.

 

...Not exactly in this sense, but hey, I'll take my wins where I can get 'em :xx:.

 

I'm sure this mystery could be abruptly solved pending Turtle's restriction to change his DOB :D.

 

Some mysteries are best left unsolved though :xx:...

Posted

Alice: That would be very nice. I’m sorry I interrupted your birthdayparty... uh, thank you.

March Hare: Birthday? Hahaha! My dear child, this is not a birthdayparty!

Mad Hatter: Of course not! Hehehe! This is an unbirthdayparty!

Alice: Unbirthday? Why, I’m sorry, but I don’t quite understand.

March Hare: It’s very simple. Now, thirty days have sept- no, when... an unbirthday, if you have a birthday then you... haha... she doesn’t know what an unbirthday is!

Mad Hatter: How silly! Ha HA Ha Ha! Ah-hum... I shall ellusinate! Now statistics prove, prove that you’ve one birthday.

March Hare: Imagine, just one birthday every year.

Mad Hatter: Ahhh, but there are 364 unbirthdays!

March Hare: Precisely why we’re gathered here to cheer!

Alice: Why, then today is my unbirthday too!

March Hare: It is?

Mad Hatter: What a small world this is.

 

Merry Unbirthday Turtle!

 

Tooot! :eek2:

Buffy

Posted

___Thank you all for your best wishes. :xx: :eek2: :D :D :xx: :xx: As I see by the Hypography Calendar no one has a birthday today, I deduce it is my un-birthday as Buffy observed. I have un-bought gifts for you all on this audatiously auspicious occasion & welcome you to un-celebrate again for the first time. :xx:

Posted

Well, I've been missing a lot of fun here, happy nth birthday, T! :eek2:

 

Oh well. I'll find another base that would make it a palindrome... eventually.
For bases in which 1898 is a two digit palindrome, (any factor of 1898 except 2) - 1. Easy, 1898 = 2*13*73.

 

a(x + 1) = N. => x = 12, 72, 25, 145, 948, 1897

 

For three digits, any integer x that solves:

 

a(x^2 + 1) + bx = N

 

with integer a and b. Trickier. Perhaps we've found new reference problems of cryptographic use? :xx: :xx: :D

Posted

:xx:

 

I was neglecting the condition x > a (and :xx:!!! :eek2:

 

For two digits it implies factors greater than root of N: bases 72, 145, 948.

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