Specifically for coldtortuga

[pmb]

A variation on a previous theme:

Base	Number	Number in Base 10
2	12	1
3	23	2
4	3124	54
5	4135	108
6	4126	152
7	651427	16200
8	76251348	2042460
9	82715369	4416720
10	986731210	9867312
Still churning - these O(nn) algorithms really soak up the CPU time... (I later hit Ctrl-C, so all numbers after this point are from coldtortuga)
11	A9876241311	2334364200
12	B935217612	421877610
13	CBA9584721313	1779700673520

Comments

[coldtortuga.livejournal.com]

Cool! That's a neat generalization :-)

(I'm just now catching up on lj after 2 weeks at my parents' home in Alaska. They only have internet connectivity via the phone line, e.g., "[ring ring ring] Hey Jen, are you near your mom's computer? Could you look up the World Cup groups and read them off to me, pretty pretty please??")

My code spat out the base-eleven answer in a few minutes (A98762413₁₁ = 2334364200₁₀) but it's been cranking for a couple hours now on base-twelve. The numbers are big enough to require Python "long" integers, which are waaaaay slower than native-hardware integers; I probably need a thorough re-writing of my generators to avoid so many multiplications and function-calls.

[coldtortuga.livejournal.com]

Somewhat disturbingly, my code reports B9352176₁₂ = 421877610₁₀ for base-twelve. Hmmmm... [taps teeth]

[pmb.livejournal.com]

Makes sense - you can't have a 0 as the final digit, which means that you can't have a multiple of 4 *and* a multiple of 3 in there, so either 4 and 8 are out or 3,6, and 9 are. Which means that you can have at most 9 digits. Why you can't have an A in there, I'm less sure, particularly since it is definitely divisible by A, as it is divisible by both 2 and 5.

[pmb.livejournal.com]

(note that the intuition I gave for 12 means that 13 will most likely be some friggin huge number, due to its primeness)

[coldtortuga.livejournal.com]

For base thirteen: CBA95847213₁₃ = 1779700673520₁₀. Good intuitin' :)