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

Author

Rémy Sigrist, May 07 2017

Keywords

• nonn
• look

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.