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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
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 (list; graph; refs; listen; history; text; internal format)
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

MATHEMATICA

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

CROSSREFS

Cf. A003463, A083065, A153773, A153776.

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

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Last modified June 18 07:06 EDT 2019. Contains 324203 sequences. (Running on oeis4.)