cyclic and pentagonal square triangular numbers
Eric W. Weisstein
eww at wolfram.com
Thu Sep 4 16:50:30 CEST 2003
1. I *was* missing something. Here are the terms I get for counts of
cyclic numbers less than 10^n:
%S A086018 0, 1, 9, 60, 467, 3617, 25883, 248881, 2165288, 19016617,
%T A086018 170169241
All but the last have been confirmed (or were computed first) by Ed Pegg
and Jud McCranie. Using the last term gives the fraction of cyclic
numbers out of all primes less than 10^10 as 0.3739551; Artin's constant
is 0.3739558136...
2. Is it known/can it be proven that there are no pentagonal square
triangular numbers other than 1? There don't seem to be any $<5.7\times
10^{2858}$..
Cheers,
-E
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