%I #2 Mar 31 2012 10:28:54

%S 2,32,41,101,161,185,206,215,230,251,290,311,326,335,356,395,416,446,

%T 461,521,566,611,626,641,656,740,860,866,926,941,956,965,1025,1055,

%U 1076,1091,1130,1151,1241,1256,1271,1286,1361,1370,1385,1391,1436,1451,1466

%N Positive integers b for which the Diophantine equation f = (b^(2n) - b^n + 8n^2 - 2) / (2n * (2n + 1)) has at least ten solutions for n <= 10000, n is never divisible by 5, and 2n + 1 is prime

%C When b = 2, there are 105 solutions less than 10000, and in this case, the sequence of n is dominated by primes: only five of these are composite. The average difference between successive composite terms is near the magnitude of n. n and 2n + 1 account for roughly 3% of primes less than 20 billion. For other bases, n is almost always composite.

%C There are 31 solutions when b = 1286.

%Y Cf. A158034, A158035, A158036

%Y Cf. A160556

%K nonn

%O 1,1

%A _Reikku Kulon_, May 19 2009