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 A268175 #24 Nov 16 2024 21:34:54
%S A268175 2,2,4,6,12,82,14,22,244,44,120,94,1010,764,834,1076,516,3252,1384,
%T A268175 1664,7040,6104,20942,14344,37142,12522,12554,64160,32172,44460,49400,
%U A268175 291726
%N A268175 Smallest number k such that k*(2^(2*A000043(n))-1)+1 is prime.
%C A268175 The numbers k*(2^(2*A000043(n))-1)+1 may be written as k*(2^A000043(n)-1)*(2^A000043(n)+1)+1 or k*Mersenne(n)*(Mersenne(n)+2)+1 and so may be proved primes.
%C A268175 All the numbers a(n)*(2^(2*A000043(n))-1)+1 for n=1 to 32 have been proved to be primes.
%e A268175 2*(2^(2*2)-1)+1 = 31 (prime) and A000043(1) = 2, so a(1) = 2.
%e A268175 2*(2^(2*3)-1)+1 = 127 (prime) and A000043(2) = 3, so a(2) = 2.
%t A268175 A000043 = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657};
%t A268175 lst = {}; maxk = 5000; maxn = 15;
%t A268175 For[n = 1, n ≤ maxn, n++,
%t A268175 For[k = 0, k ≤ maxk, k++,
%t A268175 If[PrimeQ[k*(2^(2*A000043[[n]]) - 1) + 1], AppendTo[lst, k]; Break[]]
%t A268175 ]
%t A268175 ];
%t A268175 lst (* _Robert Price_, Apr 05 2016 *)
%Y A268175 Cf. A000043.
%K A268175 nonn,more,hard
%O A268175 1,1
%A A268175 _Pierre CAMI_, Jan 28 2016