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