A286343 - OEIS

%I #16 Jun 14 2017 02:46:59

%S 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,

%T 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,

%U 6,14,24,3,15,7,16,25,2,17,26,18,19,8,20,27,4,21

%N 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.

%C 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).

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

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

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

%C 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).

%H Rémy Sigrist, <a href="/A286343/b286343.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A286343/a286343.txt">C program for A286343</a>

%Y Cf. A000045, A199088.

%K nonn,look

%O 1,4

%A _Rémy Sigrist_, May 07 2017