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 A357057 #64 Oct 02 2022 00:10:41 %S A357057 3,3,3,5,5,7,11,11,13,17,19,19,23,29,31,37,37,41,43,47,53,59,59,61,67, %T A357057 71,73,79,83,83,89 %N A357057 a(n) = A356886(2^n+1)/A356886(2^n-1). %C A357057 All terms are odd primes; some of them are repeated. %C A357057 Conjecture: This sequence has the pattern: a prime repeated, a run of m times primes standing alone, the next prime repeated, a run of m+1 times primes standing alone, ... . All primes will be repeated once or follow in sequence. We know that if A356886(2^n-1) = p1 then A356886(2^n+1) will be p1*p2. p2 will be the smallest possible prime such that p1*p2 is not yet in the sequence A356886, thus p2 = a(n). Let p1*pn be already in A356886 and pn < p2, then we know that p1*pn will be on a position A356886(2^n-(2^(k+1)-2)) with some k > 0. This should explain this pattern. - _Thomas Scheuerle_, Sep 14 2022 %Y A357057 Cf. A000051, A000225, A356886. %Y A357057 Cf. also A065091 (odd primes). %K A357057 nonn,more %O A357057 1,1 %A A357057 _Paul Curtz_, Sep 09 2022 %E A357057 a(14)-a(24) from _Michel Marcus_, Sep 13 2022 %E A357057 a(25)-a(31) from _Chai Wah Wu_, Oct 01 2022