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 A363016 #26 May 16 2023 08:13:23 %S A363016 3,6,24,77,378,1395,1395,1395,1395,31798,61457,240748,800583,804584, %T A363016 804584,804584,16118548,16138563,16138563,56307979,56307979,56307979, %U A363016 56307979,56307979,3511121443,3511121443,26284355567,26284355567,26284355567,118027458557,118027458557,118027458557,118027458557 %N A363016 a(n) is the least integer k such that the k-th, (k+1)-th, ..., (k+n-1)-th primes are congruent to 1 mod 4. %C A363016 a(n) is also the minimal rank where n consecutive 1's appear in A023512. %C A363016 The sequence is infinite by Shiu's theorem. %H A363016 D. K. L. Shiu, <a href="http://dx.doi.org/10.1112/S0024610799007863">Strings of Congruent Primes</a>, J. Lond. Math. Soc. 61 (2) (2000) 359-373. %F A363016 a(n) = A000720(A057624(n)). - _Amiram Eldar_, May 13 2023 %e A363016 For n=3, a(3) = 24 because prime(24)+1=90, prime(25)+1=98, and prime(26)+1=102 are the first 3 consecutive primes p such that p+1 is divisible by 2 and not by 4. %Y A363016 Cf. A000720, A057624, A023512. %Y A363016 Cf. A363017 (3 mod 8). %K A363016 nonn %O A363016 1,1 %A A363016 _Léo Gratien_, May 13 2023