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 A355025 #9 Jul 03 2022 20:11:31
%S A355025 2,5,23,19,37,47,79,61,107,89,149,103,163,131,191,173,233,229,317,257,
%T A355025 331,271,359,313,373,383,401,397,443,439,457,467,499,509,541,523,569,
%U A355025 593,653,607,709,677,751,691,821,719,863,733,877,761
%N A355025 a(1)=2; for n > 1, a(n) is the least new prime such that a(n-1) + a(n) is a multiple of 7.
%F A355025 a(n) = A045392((n+1)/2) if n is odd, A045458(n/2) if n is even. - _Jon E. Schoenfield_, Jun 15 2022
%e A355025 2 + 3 = 5 is not a multiple of 7, but 2 + 5 = 7 is, so a(2) = 5.
%e A355025 5 + 2 = 7 is a multiple of 7, but 2 is already a term; 5 + 3 = 8, 5 + 7 = 12, ..., 5 + 19 = 24 are not multiples of 7, but 5 + 23 = 28 is, so a(3) = 23.
%e A355025 23 + 5 = 28 is a multiple of 7, but 5 is already a term; 19 is the next prime p such that 7 divides 23 + p, so a(4) = 19.
%t A355025 s = {2}; Do[p = 3; a = s[[-1]]; While[MemberQ[s, p] || Mod[a + p, 7] != 0, p = NextPrime[p]]; AppendTo[s, p], {100}]; s
%Y A355025 Cf. A045392, A045458.
%K A355025 nonn
%O A355025 1,1
%A A355025 _Zak Seidov_, Jun 15 2022