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 A287218 #23 Mar 11 2025 04:41:40
%S A287218 1,1,3,1,1,2,3,9,12,8,3,4,3,1,36,25,8,12,19,21,3,12,19,40,9,14,1,14,2,
%T A287218 18,81,56,49,38,38,26,3,33,103,12,67,12,11,8,48,79,2,43,136,82,12,46,
%U A287218 78,31,117,126,34,4,27,49,83,3,57,234,12,10,116,128,53,13
%N A287218 a(n) = smallest k such that (6*k-3)*2^prime(n) - 1 is prime.
%C A287218 For n from 1 to 2000, a(n)/prime(n) is always < 1.8.
%C A287218 As N increases, (Sum_{n=1..N} a(n)) / (Sum_{n=1..N} prime(n)) tends to log(2)/3; this is consistent with the prime number theorem as the probability that x*2^n-1 is prime with odd x divisible by 3 is ~ 3/(n*log(2)) and after n*log(2)/3 try (n*log(2)/3)*(3/(n*log(2))) = 1.
%H A287218 Pierre CAMI, <a href="/A287218/b287218.txt">Table of n, a(n) for n = 1..2000</a>
%F A287218 a(n) = A285808(A000040(n)).
%t A287218 sk[n_]:=Module[{k=1,t=2^Prime[n]},While[!PrimeQ[(6k-3)*t-1],k++];k]; Array[ sk,70] (* _Harvey P. Dale_, Nov 14 2018 *)
%Y A287218 Subsequence of A285808.
%Y A287218 Cf. A284325, A284631.
%K A287218 nonn
%O A287218 1,3
%A A287218 _Pierre CAMI_, May 22 2017