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.
%I A160556 #4 Jun 02 2025 01:41:43 %S A160556 2,8,14,17,26,29,32,38,41,47,50,59,62,64,65,68,74,77,83,89,95,98,101, %T A160556 104,110,119,122,128,131,134,137,140,143,149,152,155,161,164,167,173, %U A160556 179,182,185,188,194,197,200,206,209,212,215,218,221,224,227,230,233 %N 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. %C A160556 For these equations (not exclusively), the sequences of 2n + 1 are dominated by primes. %C A160556 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. %C A160556 The next most productive values of b less than 1000 are 509 (41 solutions) and 824 (40 solutions). %C A160556 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. %Y A160556 Cf. A158034, A158035, A158036 %Y A160556 Cf. A160557 %K A160556 easy,nonn %O A160556 1,1 %A A160556 _Reikku Kulon_, May 19 2009