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A153777 Sequence S such that 1 is in S and if x is in S, then 5x-1 and 5x+1 are in S. 1

%I

%S 1,4,6,19,21,29,31,94,96,104,106,144,146,154,156,469,471,479,481,519,

%T 521,529,531,719,721,729,731,769,771,779,781,2344,2346,2354,2356,2394,

%U 2396,2404,2406,2594,2596,2604,2606,2644,2646,2654,2656,3594,3596,3604

%N Sequence S such that 1 is in S and if x is in S, then 5x-1 and 5x+1 are in S.

%C Subsequences include A003463, A083065.

%C 1st generation: 1

%C 2nd generation: 4, 6

%C 3rd generation: 19, 21, 29, 31

%C 4th generation: 94, 96, 104, 106, 144, 146, 154, 156

%C Does every generation contain p or 2p for some prime p?

%H Harvey P. Dale, <a href="/A153777/b153777.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(5^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)/5^(n-1)*Pi/2) = 0. - _Gevorg Hmayakyan_, Jan 15 2017

%t nxt[n_]:=Flatten[5#+{1,-1}&/@n]; Union[Flatten[NestList[nxt,{1},5]]] (* _Harvey P. Dale_, Dec 25 2012 *)

%Y Cf. A003463, A083065, A153773, A153776.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 02 2009

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Last modified July 20 05:37 EDT 2019. Contains 325168 sequences. (Running on oeis4.)