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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A160556 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.

Original entry on oeis.org

2, 8, 14, 17, 26, 29, 32, 38, 41, 47, 50, 59, 62, 64, 65, 68, 74, 77, 83, 89, 95, 98, 101, 104, 110, 119, 122, 128, 131, 134, 137, 140, 143, 149, 152, 155, 161, 164, 167, 173, 179, 182, 185, 188, 194, 197, 200, 206, 209, 212, 215, 218, 221, 224, 227, 230, 233
Offset: 1

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Author

Reikku Kulon, May 19 2009

Keywords

Comments

For these equations (not exclusively), the sequences of 2n + 1 are dominated by primes.
When b = 2, there are 105 solutions with n less than 10000, and in this case, the sequence of n is also dominated by primes: only five of these are composite. The average difference between successive composite terms is near the magnitude of n. No composite values of 2n + 1 have been found. n and 2n + 1 account for roughly 3% of primes less than 20 billion. For other bases, n is almost always composite, and 2n + 1 is almost always prime.
The next most productive values of b less than 1000 are 509 (41 solutions) and 824 (40 solutions).
Bases that produce a greater or equal number of solutions than smaller bases, except 2, often have ones digit 4 or 9. Values of n associated with composite 2n + 1 are often divisible by 5.

Crossrefs

Cf. A158034, A158035, A158036
Cf. A160557
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