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 A081858 #33 Mar 03 2024 19:24:33
%S A081858 0,3,8,11,15,20,23,35,36,39,44,48,51,56,63,68,75,83,95,96,99,111,116,
%T A081858 119,120,128,131,135,140,155,156,168,170,176,179,183,191,200,204,215,
%U A081858 216,219,224,228,231,239,243,251,260,280,284,288,296,299,300,303,308
%N A081858 Numbers k such that 2*k+1 divides 2^k-1.
%C A081858 From _Chris Boyd_, Mar 16 2014: (Start)
%C A081858 n is a term if and only if n=0, 2n+1 is a prime of the form 8k+-1, or 2n+1 is an Euler pseudoprime satisfying 2^n == 1 mod 2n+1.
%C A081858 Case 1: 0 is a term. Case 2, 2n+1 prime: by Euler's criterion and the quadratic character of 2, 2^n == 1 mod 2n+1 only if 2n+1 is of the form 8k+-1. Case 3, 2n+1 composite: 2^n == 1 mod 2n+1 only if 2n+1 is one of the subset of Euler pseudoprimes satisfying 2^n == 1 mod 2n+1.
%C A081858 The first term for which 2n+1 is a qualifying Euler pseudoprime is n=170.
%C A081858 The first Euler pseudoprime that does not correspond to a term is 3277, because 2^((3277-1)/2) == -1 mod 3277. (End)
%H A081858 Amiram Eldar, <a href="/A081858/b081858.txt">Table of n, a(n) for n = 1..10000</a>
%F A081858 k such that A002326(k)|k: since 2^k == 1 mod 2*k+1, k must be a multiple of the order of 2 mod 2*k+1.
%t A081858 Join[{0}, Select[Range[300], PowerMod[2, #, 2*# + 1] === 1 &]] (* _Amiram Eldar_, Jun 02 2022 *)
%o A081858 (PARI) isok(n) = !((2^n-1) % (2*n+1)); \\ _Michel Marcus_, Dec 04 2013
%o A081858 (PARI) for(n=0,400,if(n%znorder(Mod(2,2*n+1))==0,print1(n","))) \\ _Chris Boyd_, Mar 16 2014, after _Michael Somos_ in A002326
%Y A081858 Cf. A002326, A014664.
%K A081858 nonn
%O A081858 1,2
%A A081858 _Benoit Cloitre_, Apr 11 2003
%E A081858 Formula corrected by _Chris Boyd_, Mar 16 2014