%I
%S 1,3,5,11,13,19,21,43,45,51,53,75,77,83,85,171,173,179,181,203,205,
%T 211,213,299,301,307,309,331,333,339,341,683,685,691,693,715,717,723,
%U 725,811,813,819,821,843,845,851,853,1195,1197,1203,1205,1227,1229,1235
%N Sequence S such that 1 is in S and if x is in S, then 4x1 and 4x+1 are in S.
%C Does every generation after the initial 1 contain a prime?
%H Ivan Neretin, <a href="/A147992/b147992.txt">Table of n, a(n) for n = 1..10000</a>
%H Gevorg Hmayakyan, <a href="http://math.stackexchange.com/questions/1918281/generalizingatrigidentity">Trig identity for a(n)</a>
%F Product_{j=0..n1} cos(4^j) = 2^(n+1)*Sum_{i=2^(n1)..2^n1} cos(a(i)).  _Gevorg Hmayakyan_, Jan 15 2017
%F Sum_{i=2^(n1)..2^n1} cos(a(i)/4^(n1)*Pi/2) = 0.  _Gevorg Hmayakyan_, Jan 15 2017
%e 0th generation: 1
%e 1st generation: 3 5
%e 2nd generation: 11 13 19 21
%K nonn
%O 1,2
%A _Clark Kimberling_, Dec 07 2008
