A160557 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.

2, 32, 41, 101, 161, 185, 206, 215, 230, 251, 290, 311, 326, 335, 356, 395, 416, 446, 461, 521, 566, 611, 626, 641, 656, 740, 860, 866, 926, 941, 956, 965, 1025, 1055, 1076, 1091, 1130, 1151, 1241, 1256, 1271, 1286, 1361, 1370, 1385, 1391, 1436, 1451, 1466

Offset

1,1

Comments

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.

There are 31 solutions when b = 1286.

Links

Table of n, a(n) for n=1..49.

Crossrefs

Cf. A158034, A158035, A158036

Cf. A160556

Sequence in context: A022378 A306950 A193419 * A103028 A139732 A037313

Adjacent sequences: A160554 A160555 A160556 * A160558 A160559 A160560

Keyword

nonn

Author

Reikku Kulon, May 19 2009

Status

approved