

A035614


Horizontal paraFibonacci sequence: says which column of Wythoff array (starting column count at 0) contains n.


10



0, 1, 2, 0, 3, 0, 1, 4, 0, 1, 2, 0, 5, 0, 1, 2, 0, 3, 0, 1, 6, 0, 1, 2, 0, 3, 0, 1, 4, 0, 1, 2, 0, 7, 0, 1, 2, 0, 3, 0, 1, 4, 0, 1, 2, 0, 5, 0, 1, 2, 0, 3, 0, 1, 8, 0, 1, 2, 0, 3, 0, 1, 4, 0, 1, 2, 0, 5, 0, 1, 2, 0, 3, 0, 1, 6, 0, 1, 2, 0, 3
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OFFSET

0,3


COMMENTS

This is probably the same as the "Fibonacci ruler function" mentioned by Knuth.  N. J. A. Sloane, Aug 03 2012


REFERENCES

D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.3, p. 82, solution to Problem 179.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Casey Mongoven, Sonification of multiple Fibonaccirelated sequences, Annales Mathematicae et Informaticae, 41 (2013) pp. 175192.
N. J. A. Sloane, Classic Sequences


FORMULA

The segment between the first M and the first M+1 is given by the segment before the first M1.


MATHEMATICA

max = 81; wy = Table[(nk)*Fibonacci[k] + Fibonacci[k+1]*Floor[ GoldenRatio*(n  k + 1)], {n, 1, max}, {k, 1, n}]; a[n_] := Position[wy, n][[1, 2]]1; Table[a[n], {n, 1, max}] (* JeanFrançois Alcover, Nov 02 2011 *)


PROG

(Haskell)
a035614 = a122840 . a014417 . (+ 1)  Reinhard Zumkeller, Mar 10 2013


CROSSREFS

Cf. A019586, A035513, A035614.
Sequence in context: A065134 A088673 A236138 * A212138 A133735 A238801
Adjacent sequences: A035611 A035612 A035613 * A035615 A035616 A035617


KEYWORD

nonn,nice,easy


AUTHOR

J. H. Conway and N. J. A. Sloane.


STATUS

approved



