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 A201914 #23 Sep 08 2022 08:46:01
%S A201914 2,5,3,7,47,31,191,127,1279,3583,5119,6143,20479,8191,81919,294911,
%T A201914 1114111,131071,786431,524287,17825791,14680063,138412031,109051903,
%U A201914 654311423,1912602623,738197503,2818572287,7247757311,3758096383,228707008511,2147483647
%N A201914 Least prime p such that p+1 is divisible by 2^n and not by 2^(n+1).
%C A201914 See A126717 for the least k such that k*2^n-1 is prime.
%C A201914 For every n >= 1 there are infinitely many prime numbers p such that p + 1 is divisible by 2^n and not by 2^(n + 1). - _Marius A. Burtea_, Mar 10 2020
%D A201914 Laurențiu Panaitopol, Alexandru Gica, Arithmetic problems and number theory, Ed. Gil, Zalău, (2006), ch. 13, p. 78, pr. 5 (in Romanian).
%H A201914 Donovan Johnson, <a href="/A201914/b201914.txt">Table of n, a(n) for n = 0..1000</a>
%t A201914 Table[k = 1; While[p = k*2^n - 1; ! PrimeQ[p], k = k + 2]; p, {n, 0, 40}]
%o A201914 (Magma) a:=[]; for n in [0..31] do k:=1; while not IsPrime(k*2^n-1) do k:=k+2; end while; Append(~a,k*2^n-1); end for; a; // _Marius A. Burtea_, Mar 10 2020
%Y A201914 Cf. A008864 (primes + 1), A057775 (p-1 case), A126717.
%Y A201914 For n>0, sequence is first term of A002144, A007520, A141194, A142041, A142939, ...
%K A201914 nonn
%O A201914 0,1
%A A201914 _T. D. Noe_, Dec 27 2011