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A104626
Numbers having three 1's in their base-phi representation.
5
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
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
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
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