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 A147993 #19 Jan 30 2023 18:49:07
%S A147993 1,5,7,29,31,41,43,173,175,185,187,245,247,257,259,1037,1039,1049,
%T A147993 1051,1109,1111,1121,1123,1469,1471,1481,1483,1541,1543,1553,1555,
%U A147993 6221,6223,6233,6235,6293,6295,6305,6307,6653,6655,6665,6667,6725,6727,6737,6739
%N A147993 Sequence S such that 1 is in S and if x is in S, then 6x-1 and 6x+1 are in S.
%C A147993 Does every generation after the initial 1 contain a prime?
%H A147993 Ivan Neretin, <a href="/A147993/b147993.txt">Table of n, a(n) for n = 1..10000</a>
%F A147993 Product_{j=0..n-1} cos(6^j) = 2^(-n+1)*Sum_{i=2^(n-1)..2^n-1} cos(a(i)). - _Gevorg Hmayakyan_, Jan 15 2017
%F A147993 Sum_{i=2^(n-1)..2^n-1} cos((a(i)/6^(n-1))*(Pi/2)) = 0. - _Gevorg Hmayakyan_, Jan 15 2017
%F A147993 a(n) = 2*A032806(n-1) + 1 for n>=2. - _Alois P. Heinz_, Jan 29 2023
%e A147993 0th generation: 1
%e A147993 1st generation: 5 7
%e A147993 2nd generation: 29 31 41 43
%t A147993 sss[n_]:={6n-1,6n+1}; NestList[Sort[Flatten[sss[#]]]&,{1},5]//Flatten (* _Harvey P. Dale_, Aug 06 2018 *)
%Y A147993 Cf. A032806.
%Y A147993 Column k=6 of A360099.
%K A147993 nonn
%O A147993 1,2
%A A147993 _Clark Kimberling_, Dec 07 2008