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

Author

Clark Kimberling, Jan 02 2009

Keywords

• nonn

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)

Crossrefs

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

Column k=5 of A360099.

Programs

Mathematica

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

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