A104626 Numbers having three 1's in their base-phi representation.

4, 5, 6, 8, 19, 48, 124, 323, 844, 2208, 5779, 15128, 39604, 103683, 271444, 710648, 1860499, 4870848, 12752044, 33385283, 87403804, 228826128, 599074579, 1568397608, 4106118244, 10749957123, 28143753124, 73681302248

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Jeffrey Shallit, Proving Properties of phi-Representations with the Walnut Theorem-Prover, arXiv:2305.02672 [math.NT], 2023.

Eric Weisstein's World of Mathematics, Phi Number System

Wikipedia, Golden ratio base

Formula

{n: A055778(n) = 3}. - R. J. Mathar, Sep 05 2010

a(n) = Lucas(2*n-4) + 1, for n>3. - Ralf Stephan, Nov 13 2010

Mathematica

Join[{4, 5, 6}, Table[LucasL[2*n-4] + 1, {n, 4, 50}]] (* G. C. Greubel, Aug 13 2018 *)

Prog

(PARI) for(n=1, 50, print1(if(n==1, 4, if(n==2, 5, if(n==3, 6, 1 + fibonacci(2*n-3) + fibonacci(2*n-5)))), ", ")) \\ G. C. Greubel, Aug 13 2018
(Magma) [4, 5, 6] cat [1 + Fibonacci(2*n-3) + Fibonacci(2*n-5): n in [4..50]]; // G. C. Greubel, Aug 13 2018

Crossrefs

Cf. A005248, A104627, A104628, A065034.

Sequence in context: A006756 A067652 A080805 * A242955 A086726 A078885

Adjacent sequences: A104623 A104624 A104625 * A104627 A104628 A104629

Keyword

nonn

Author

Eric W. Weisstein, Mar 17 2005

Extensions

Terms 5 and 6 added by Jaroslav Krizek, May 25 2010

Edited by R. J. Mathar, Sep 05 2010

Status

approved