A367491 - OEIS

%I #7 Nov 20 2023 08:15:37

%S 2,5,7,9,10,13,15,18,20,22,23,26,28,30,31,34,36,38,39,41,43,44,47,49,

%T 52,54,56,57,60,62,64,65,68,70,73,75,77,78,81,83,85,86,89,91,93,94,96,

%U 98,99,102,104,107,109,111,112,115,117,119,120,123,125,127,128

%N Lexicographically least increasing sequence, starting with 2, such that no two terms (possibly identical) sum to a Fibonacci number.

%C There is an 8-state Fibonacci automaton that accepts the Zeckendorf representation of n if and only if n belongs to the sequence.

%e 6 is not in the sequence, since if it were, 6+2 = 8, a Fibonacci number.

%Y Cf. A005652, A005653. This sequence allows the same term to be used twice in the sum, whereas in the other two sequences, the terms must be distinct.

%K nonn

%O 1,1

%A _Jeffrey Shallit_, Nov 20 2023