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 A361919 #13 Apr 01 2023 23:32:03 %S A361919 1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,2,2,2,2,2,2,2,1,2,4,4,3,2,1,1,3,2,3,2, %T A361919 3,2,3,3,3,2,3,3,3,2,2,1,3,5,4,3,3,3,2,3,3,4,4,3,3,2,1,3,3,3,2,2,4,4, %U A361919 4,3,3,3,4,3,4,3,3,3,3,4,5,4,4,4,5,5 %N A361919 The number of primes > A000040(n) and <= (A000040(n)^c + 1)^(1/c), where c = 0.567148130202... is defined in A038458. %C A361919 Let c = 0.567148130202... (see A038458), the solution to 127^x - 113^x = 1. c is conjectured by Smarandache to be the smallest real number x such that A000040(n+1)^x - A000040(n)^x = 1 has a solution. This conjecture is equivalent to saying that the terms of the present sequence are always positive, but that if c were replaced by a larger real number, there would be zeros in the sequence. However, note that a(30) is not the last occurrence of 1: a(46) = a(61) = 1 as well. %H A361919 Hal M. Switkay, <a href="/A361919/b361919.txt">Table of n, a(n) for n = 1..665</a> %H A361919 F. Smarandache, <a href="http://arxiv.org/abs/0707.2584">Conjectures which generalize Andrica's conjecture</a>, arXiv:0707.2584 [math.GM], 2007; Octogon 7:1 (1999), pp. 173-176. %e A361919 a(30) is the number of primes > A000040(30), which is 113, and <= (113^c + 1)^(1/c) = 127. This relatively large interval contains only the prime 127. %Y A361919 Cf. A000040, A038458. %K A361919 nonn %O A361919 1,7 %A A361919 _Hal M. Switkay_, Mar 29 2023