

A249783


Smallest index of a Fibonaccilike sequence containing n, see comments.


5



0, 1, 1, 1, 2, 1, 2, 3, 1, 3, 2, 3, 4, 1, 4, 3, 2, 5, 3, 5, 4, 1, 6, 4, 3, 5, 2, 7, 5, 3, 6, 5, 4, 6, 1, 7, 6, 4, 7, 3, 5, 7, 2, 8, 7, 5, 8, 3, 6, 8, 5, 9, 4, 6, 9, 1, 7, 9, 6, 10, 4, 7, 10, 3, 8, 5, 7, 11, 2, 8, 11, 7, 9, 5, 8, 12, 3, 9, 6, 8, 10, 5, 9, 13, 4, 10, 6, 9, 11, 1, 10, 7, 9, 11, 6, 10, 12, 4, 11, 7, 10
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OFFSET

0,5


COMMENTS

Any two nonnegative integers F0 and F1 generate a Fibonaccilike sequence where for n > 1, Fn = F[n1] + F[n2]. Call F0 + F1 the "index" of such a sequence. In this sequence, a(n) is the smallest occurring index of any Fibonaccilike sequence containing n.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000
Index to sequences related to the complexity of n


FORMULA

a(n) <= A054495(n) <= n.  Charles R Greathouse IV, Nov 06 2014


EXAMPLE

For n = 0, the trivial sequence 0, 0, 0, ... has index 0.
For n = 5, the classic Fibonacci sequence 0, 1, 1, 2, 3, 5, ... contains 5 and has index 1.
For n = 7, the Lucas sequence 2, 1, 3, 4, 7, ... contains 7, and no such sequence with a smaller index contains 7.


MATHEMATICA

a[n_] := Module[{a, k, A, B}, If[n<2, Return[n]]; For[k=1, k <= n1, k++, For[a=0, a <= k1, a++, A=a; B=kA; While[B<n, {A, B} = {B, A+B}]; If[B == n, Return[k]]]]; n]; Array[a, 101, 0] (* JeanFrançois Alcover, Jan 06 2017, translated from PARI *)


PROG

(Haskell)
bi x y = if (x<y) then (x+y) else (bi y (xy))
a249783 0 = 0
a249783 n = minimum (map (bi n) [0..(n1)])
(PARI) a(n)=if(n<2, return(n)); for(k=1, n1, for(a=0, k1, my(A=a, B=kA); while(B<n, [A, B]=[B, A+B]); if(B==n, return(k)))); n \\ Charles R Greathouse IV, Nov 06 2014


CROSSREFS

If n > 0 is an element of A000045, a(n) = 1. If n > 2 is twice such an element, a(n) = 2. If n > 3 is an element of A000032 or of A022086, a(n) = 3.
Sequence in context: A082076 A231516 A048793 * A209278 A326921 A286343
Adjacent sequences: A249780 A249781 A249782 * A249784 A249785 A249786


KEYWORD

nonn,look,nice


AUTHOR

Allan C. Wechsler, Nov 05 2014


EXTENSIONS

Extended by Charles R Greathouse IV, Nov 06 2014


STATUS

approved



