A286343 For n>0, let b(n) = greatest index of n in any Fibonacci-like sequence containing n. This sequence is the ordinal transform of b.

1, 1, 1, 2, 1, 2, 3, 1, 3, 2, 4, 5, 1, 6, 3, 2, 7, 4, 8, 5, 1, 9, 6, 3, 7, 2, 10, 8, 4, 9, 10, 5, 11, 1, 12, 13, 6, 14, 3, 7, 15, 2, 16, 17, 8, 18, 4, 9, 19, 10, 20, 5, 11, 21, 1, 12, 22, 13, 23, 6, 14, 24, 3, 15, 7, 16, 25, 2, 17, 26, 18, 19, 8, 20, 27, 4, 21

Offset

1,4

Comments

A Fibonacci-like sequence f satisfies f(n+2) = f(n+1) + f(n), and is uniquely identified by its two initial terms f(0) and f(1).

For any n>0, b(n) >= 2 (as n appears at index 2 in the Fibonacci-like sequence with initial terms n and 0).

Conjecturally, for any n>1, b(n) = A199088(n).

a(A000045(n)) = 1 for any n>0.

The ordinal transform mentioned is the one described in A002260: the ordinal transform of a sequence b(n) is the sequence t(n) = number of values in b(1),...,b(n) which are equal to b(n).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, C program for A286343

Crossrefs

Cf. A000045, A199088.

Sequence in context: A326921 A370408 A358090 * A368399 A075106 A196935

Adjacent sequences: A286340 A286341 A286342 * A286344 A286345 A286346

Keyword

nonn,look

Author

Rémy Sigrist, May 07 2017

Status

approved