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 A349642 #10 Dec 05 2021 14:32:08 %S A349642 2,2,2,17,347,2903,15373,128981,19641263,245333213,245333213, %T A349642 27797667517,68439250465123,68439250465123 %N A349642 Smallest prime such that the next n prime gaps are in arithmetic progression. %C A349642 Equivalently, a(n) is the smallest prime p = prime(k) such that there is a polynomial f of degree at most 2 such that f(j) = prime(j) for k <= j <= k + n. %C A349642 Any sequence of at most 2 terms is considered to be a degenerate arithmetic progression, so a(n) = 2 (the smallest prime) for n <= 2. %C A349642 a(n) is the smallest prime p = prime(k) such that A036263(k) = A036263(k+1) = ... = A036263(k+n-2). %e A349642 The three prime gaps following the prime 17 are 2, 4, and 6, which are in arithmetic progression. This is not true for any smaller prime, so a(3) = 17. %e A349642 The eight prime gaps following the prime 19641263 are 20, 18, 16, 14, 12, 10, 8, and 6, which are in arithmetic progression. This is not true for any smaller prime, so a(8) = 19641263. %Y A349642 From n = 3, second row of A349644. %Y A349642 Cf. A001223, A006560, A036263, A348927. %K A349642 nonn,more %O A349642 0,1 %A A349642 _Pontus von Brömssen_, Nov 23 2021 %E A349642 a(12)-a(13) from _Martin Ehrenstein_, Dec 05 2021