OFFSET
0,2
COMMENTS
a(n)=least k such that s(k)=n, where s=A026350.
a(n)=position of n-th 1 in A096270.
From Wolfdieter Lang, Jun 27 2011: (Start)
a(n) = A(n)+1, with Wythoff sequence A(n)=A000201(n), n>=1, and A(0)=0.
a(n) = -floor(-n*phi). Recall that floor(-x) = -(floor(x)+1) if x is not integer and -floor(x) otherwise.
An exhaustive and disjoint decomposition of the integers is given by the following two Wythoff sequences A' and B: A'(0):=-1 (not 0), A'(-n):=-a(n)=-(A(n)+1), n>=1, A'(n) = A(n), n>=1, and B(-n):=-(B(n)+1)= -A026352(n), n>=1, with B(n)=A001950(n), n>=1, and B(0)=0.
(End)
LINKS
Carmine Suriano, Table of n, a(n) for n = 0..10000
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.
J. H. Conway and N. J. A. Sloane, Notes on the Para-Fibonacci and related sequences
Eric Friedman, Scott M. Garrabrant, Ilona K. Phipps-Morgan, A. S. Landsberg and Urban Larsson, Geometric analysis of a generalized Wythoff game, in Games of no Chance 5, MSRI publ. Cambridge University Press, 2019.
N. J. A. Sloane, Classic Sequences
MATHEMATICA
Table[Floor[n*GoldenRatio] + 1, {n, 0, 100}] (* T. D. Noe, Apr 15 2011 *)
PROG
(Haskell)
import Data.List (findIndices)
a026351 n = a026351_list !! n
a026351_list = findIndices odd a060142_list
-- Reinhard Zumkeller, Nov 26 2012
(Python)
from math import isqrt
def A026351(n): return (n+isqrt(5*n**2)>>1)+1 # Chai Wah Wu, Aug 17 2022
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved