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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. 9

%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 4x-1 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/generalizing-a-trig-identity">Trig identity for a(n)</a>

%F 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 Sum_{i=2^(n-1)..2^n-1} cos(a(i)/4^(n-1)*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

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Last modified July 23 15:58 EDT 2019. Contains 325258 sequences. (Running on oeis4.)