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 A382249 #25 Apr 25 2025 20:41:22 %S A382249 23,19,17,13,11,7,5,97,89,877,863,859,857,853,839,829,827,823,821,811, %T A382249 809,3954889,15186331,15186323,15186319,77011331,77011303,77011289, %U A382249 288413249,288413233,288413219,288413173,288413159,62585146739,114058236679,143014298851,143014298831,143014298809 %N A382249 a(n) is the smallest starting prime of a sequence of exactly n consecutive primes that are alternately of the form 6*k+1 and 6*k-1 or vice versa. %e A382249 a(1) = 23, because 23 and 29 are 2 consecutive primes such that 23 = 6*4 - 1, while 29 = 6*5 - 1. Additionally, no smaller prime possesses this property. %e A382249 a(2) = 19, because 19, 23 and 29 are 3 consecutive primes such that 19 = 6*3 + 1 and 23 = 6*4 - 1, while 29 = 6*5 - 1. Additionally, no smaller prime possesses this property. %e A382249 Table of consecutive primes %e A382249 1 [23] = 6*[4] + [-1]; %e A382249 2 [19, 23] = 6*[3, 4] + [1, -1]; %e A382249 3 [17, 19, 23] = 6*[3, 3, 4] + [-1, 1, -1]; %e A382249 4 [13, 17, 19, 23] = 6*[2, 3, 3, 4] + [1, -1, 1, -1]; %e A382249 5 [11, 13, 17, 19, 23] = 6*[2, 2, 3, 3, 4] + [-1, 1, -1, 1, -1]; %Y A382249 Cf. A057620, A057622. %K A382249 nonn %O A382249 1,1 %A A382249 _Jean-Marc Rebert_, Mar 19 2025