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A147992 Sequence S such that 1 is in S and if x is in S, then 4x-1 and 4x+1 are in S.

%I A147992 #26 Jan 30 2023 18:47:57
%S A147992 1,3,5,11,13,19,21,43,45,51,53,75,77,83,85,171,173,179,181,203,205,
%T A147992 211,213,299,301,307,309,331,333,339,341,683,685,691,693,715,717,723,
%U A147992 725,811,813,819,821,843,845,851,853,1195,1197,1203,1205,1227,1229,1235
%N A147992 Sequence S such that 1 is in S and if x is in S, then 4x-1 and 4x+1 are in S.
%C A147992 Does every generation after the initial 1 contain a prime?
%H A147992 Ivan Neretin, <a href="/A147992/b147992.txt">Table of n, a(n) for n = 1..10000</a>
%H A147992 Gevorg Hmayakyan, <a href="http://math.stackexchange.com/questions/1918281/generalizing-a-trig-identity">Trig identity for a(n)</a>
%F A147992 Product_{j=0..n-1} cos(4^j) = 2^(-n+1)*Sum_{i=2^(n-1)..2^n-1} cos(a(i)). - _Gevorg Hmayakyan_, Jan 15 2017
%F A147992 Sum_{i=2^(n-1)..2^n-1} cos(a(i)/4^(n-1)*Pi/2) = 0. - _Gevorg Hmayakyan_, Jan 15 2017
%F A147992 a(n) = 2*A032925(n-1) + 1 for n>=2. - _Alois P. Heinz_, Jan 29 2023
%e A147992 0th generation: 1
%e A147992 1st generation: 3 5
%e A147992 2nd generation: 11 13 19 21
%Y A147992 Cf. A032925.
%Y A147992 Column k=4 of A360099.
%K A147992 nonn
%O A147992 1,2
%A A147992 _Clark Kimberling_, Dec 07 2008