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 A165235 #7 Feb 16 2025 08:33:11
%S A165235 3,5,5,17,17,1607,1607,19427,2397347207,153535525937
%N A165235 Least prime p such that the n+1 numbers p + 2^k - 2, k=1..n+1, are all prime.
%C A165235 The n+1 primes have common differences of 2^k for k=1..n. For any n, the set {2^k - 2, k=1..n+1} is admissible. Hence by the prime k-tuple conjecture, an infinite number of primes p should exist for each n. Note that a(1) is the first term of the twin primes A001359 and a(2) is the first term of prime triples A022004. The a(12) term is greater than 10^12.
%H A165235 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Primek-TuplesConjecture.html">k-Tuple Conjecture</a>
%e A165235 a(5)=17 because {17,19,23,31,47,79} are 6 primes whose differences are powers of 2, and 17 is the least such prime.
%t A165235 p=3; Table[While[ !And@@PrimeQ[p+2^Range[2,n+1]-2], p=NextPrime[p]]; p, {n,8}]
%Y A165235 Cf. A000918 (2^n - 2)
%K A165235 hard,nonn
%O A165235 1,1
%A A165235 _T. D. Noe_, Sep 09 2009