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 A153777 #28 Jan 30 2023 18:48:31
%S A153777 1,4,6,19,21,29,31,94,96,104,106,144,146,154,156,469,471,479,481,519,
%T A153777 521,529,531,719,721,729,731,769,771,779,781,2344,2346,2354,2356,2394,
%U A153777 2396,2404,2406,2594,2596,2604,2606,2644,2646,2654,2656,3594,3596,3604
%N A153777 Sequence S such that 1 is in S and if x is in S, then 5x-1 and 5x+1 are in S.
%C A153777 Subsequences include A003463, A083065.
%C A153777 1st generation: 1
%C A153777 2nd generation: 4, 6
%C A153777 3rd generation: 19, 21, 29, 31
%C A153777 4th generation: 94, 96, 104, 106, 144, 146, 154, 156
%C A153777 Does every generation contain p or 2p for some prime p?
%H A153777 Harvey P. Dale, <a href="/A153777/b153777.txt">Table of n, a(n) for n = 1..10000</a>
%H A153777 Gevorg Hmayakyan, <a href="http://math.stackexchange.com/questions/1918281/generalizing-a-trig-identity">Trig identity for a(n)</a>
%F A153777 Product_{j=0..n-1} cos(5^j) = 2^(-n+1)*Sum_{i=2^(n-1)..2^n-1} cos(a(i)). - _Gevorg Hmayakyan_, Jan 15 2017
%F A153777 Sum_{i=2^(n-1)..2^n-1} cos(a(i)/5^(n-1)*Pi/2) = 0. - _Gevorg Hmayakyan_, Jan 15 2017
%F A153777 a(n) mod 2 = A030300(n). - _Alois P. Heinz_, Jan 29 2023
%t A153777 nxt[n_]:=Flatten[5#+{1,-1}&/@n]; Union[Flatten[NestList[nxt,{1},5]]] (* _Harvey P. Dale_, Dec 25 2012 *)
%Y A153777 Cf. A003463, A030300, A083065, A153773, A153776.
%Y A153777 Column k=5 of A360099.
%K A153777 nonn
%O A153777 1,2
%A A153777 _Clark Kimberling_, Jan 02 2009