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A035614 Horizontal para-Fibonacci 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 (list; graph; refs; listen; history; text; internal format)
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. - From N. J. A. Sloane, Aug 03 2012

Casey Mongoven, Sonification of multiple Fibonacci-related sequences, Annales Mathematicae et Informaticae, 41 (2013) pp. 175-192.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

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 M-1.

MATHEMATICA

max = 81; wy = Table[(n-k)*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}] (* Jean-Fran├žois 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

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Last modified November 24 07:22 EST 2014. Contains 249872 sequences.