A050141 a(n) = 2*floor((n+1)*phi) - 2*floor(n*phi) - 1 where phi = (1 + sqrt(5))/2 is the golden ratio.

3, 1, 3, 3, 1, 3, 1, 3, 3, 1, 3, 3, 1, 3, 1, 3, 3, 1, 3, 1, 3, 3, 1, 3, 3, 1, 3, 1, 3, 3, 1, 3, 3, 1, 3, 1, 3, 3, 1, 3, 1, 3, 3, 1, 3, 3, 1, 3, 1, 3, 3, 1, 3, 1, 3, 3, 1, 3, 3, 1, 3, 1, 3, 3, 1, 3, 3, 1, 3, 1, 3, 3, 1, 3, 1, 3, 3, 1, 3, 3, 1, 3, 1, 3

Offset

1,1

Comments

First differences of A050140.

The substitutions 3->1 and 1->0 carry this sequence onto the infinite Fibonacci word (A005614).

Links

Table of n, a(n) for n=1..84.

Prog

(PARI) a(n)=(n+1+sqrtint(5*(n+1)^2))\2*2 - (n+sqrtint(5*n^2))\2*2 - 1 \\ Charles R Greathouse IV, Dec 28 2017

Crossrefs

Sequence in context: A216637 A358643 A234308 * A274773 A132752 A131241

Adjacent sequences: A050138 A050139 A050140 * A050142 A050143 A050144

Keyword

nonn,base

Author

Clark Kimberling

Extensions

Name edited by Michel Marcus and Charles R Greathouse IV, Dec 28 2017

Status

approved