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 A289556 #27 Aug 04 2017 15:31:25
%S A289556 3,7,13,43,67,109,127,151,163,211,277,307,373,457,463,601,613,673,727,
%T A289556 853,919,967,1021,1117,1171,1231,1399,1471,1483,1747,1789,1933,2029,
%U A289556 2251,2311,2389,2503,2521,2557,2659,2851,2857,3019,3067,3121,3229,3583,3613,3637,3691,3697
%N A289556 Primes p such that both 5*p - 4 and 4*p - 5 are prime.
%C A289556 The terms of this sequence belong to two disjoint subsequences, namely those for which |A(5*p) - A(4*p)| = 9; (3,7,13,43,67,127,163,211,277,307,457,...), and those for which 5*A(4*p) - 3*A(5*p) = 3, (109,151,373,673,919,...), where A = A288814.
%C A289556 Note: A288814(n) = A056240(n) for all composite n.
%e A289556 P=7: 5*7 - 4 = 31, 4*7 - 5 = 23, both prime so 7 is in this sequence, and belongs to the subsequence of terms satisfying A(4*p) - A(3*p) = 9.
%e A289556 P=109: 5*109 - 4 = 541, 4*109 - 5 = 431, both prime so 109 is in this sequence, and belongs to the subsequence of terms satisfying 5*A(4*p) - 3*A(5*p) = 3.
%t A289556 Select[Prime@ Range@ 516, Times @@ Boole@ Map[PrimeQ, {5 # - 4, 4 # - 5}] > 0 &] (* _Michael De Vlieger_, Aug 02 2017 *)
%Y A289556 Cf. A259730, A288814, A290163, A290164, A056240.
%Y A289556 Intersection of A136051 and A156300. - _Michel Marcus_, Aug 04 2017
%K A289556 nonn
%O A289556 1,1
%A A289556 _David James Sycamore_, Aug 02 2017
%E A289556 More terms from _Altug Alkan_, Aug 02 2017