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, 4, 6, 19, 21, 29, 31, 94, 96, 104, 106, 144, 146, 154, 156, 469, 471, 479, 481, 519, 521, 529, 531, 719, 721, 729, 731, 769, 771, 779, 781, 2344, 2346, 2354, 2356, 2394, 2396, 2404, 2406, 2594, 2596, 2604, 2606, 2644, 2646, 2654, 2656, 3594, 3596, 3604

Offset

1,2

Comments

Subsequences include A003463, A083065.

1st generation: 1

2nd generation: 4, 6

3rd generation: 19, 21, 29, 31

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

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..10000

Gevorg Hmayakyan, Trig identity for a(n)

Formula

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

Sum_{i=2^(n-1)..2^n-1} cos(a(i)/5^(n-1)*Pi/2) = 0. - Gevorg Hmayakyan, Jan 15 2017

a(n) mod 2 = A030300(n). - Alois P. Heinz, Jan 29 2023

Mathematica

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

Crossrefs

Cf. A003463, A030300, A083065, A153773, A153776.

Column k=5 of A360099.

Sequence in context: A317584 A012928 A013160 * A034189 A024697 A024874

Adjacent sequences: A153774 A153775 A153776 * A153778 A153779 A153780

Keyword

nonn

Author

Clark Kimberling, Jan 02 2009

Status

approved