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 A127256 #6 Aug 01 2024 10:36:45 %S A127256 1,5,15,23,33,41,53,75,89,99,105,113,153,155,165,189,215,239,249,261, %T A127256 281,293,323,341,363,371,375,405,411,419,431,473,519,543,545,561,575, %U A127256 629,659,699,725,741,743,765,785,803,831,849,893,905,915,923,933,935 %N A127256 a(n) is the initial element of the sequence A(n) defined exactly like A119751 but with the additional condition that each of its elements must not be contained in any of the sequences A(k) for k < n. %C A127256 a(n)=A(n,1), the first element of each sequence A(n) defined recursively as follows. Recall that A119751 is the sequence defined recursively by a(1)=1 and a(k) is the first odd number greater than a(k-1) such that 2a(k)+1 is prime and a(k)+a(j)+1 is prime for all 1<=j<k. Let A(1)=A119751, that is, A(1,k)=A119751(k). Then A(n) is the sequence defined recursively as follows: (1) A(n,1) is the first odd number not in any A(m), 1<=m<n, such that 2A(n,1)+1 is prime. (2) A(n,k) is the first odd number greater than A(n,k-1), not in any A(m), 1<=m<n, such that 2A(n,k)+1 is prime. (3) A(n,k)+A(n,j)+1 is prime for all 1<=j<k. %e A127256 a(1)=1 is the first element of A119751=1, 3, 9, 69, 429, 4089, 86529, 513099, ... so a(2)=5 since 5 is the first odd number not in A119751 such that 2*5+1 is prime. Furthermore, A(2)=5, 11, 35, 95, 221, 551, 1271, 5705,... %Y A127256 Cf. A119751, A119752, A127257. %K A127256 nonn %O A127256 1,2 %A A127256 _Walter Kehowski_, Jan 10 2007