A242940 a(n) is the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a term of the sequence if and only if a(n) is a Fibonacci number".
1, 2, 3, 6, 7, 8, 13, 21, 22, 23, 24, 25, 34, 35, 36, 37, 38, 39, 40, 41, 55, 89, 144, 233, 377, 378, 379, 380, 381, 382, 383, 384, 610, 987, 1597
Offset: 1
Examples
a(4) cannot be 5 because that would require 4 to be a term of this sequence.