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

Author

Eric W. Weisstein, Mar 17 2005

Keywords

• nonn

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

Crossrefs

Cf. A005248, A104627, A104628, A065034.

Programs

Magma

[4,5,6] cat [1 + Fibonacci(2*n-3) + Fibonacci(2*n-5): n in [4..50]]; // G. C. Greubel, Aug 13 2018

Mathematica

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

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

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

Extensions

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

Edited by R. J. Mathar, Sep 05 2010