A367491 Lexicographically least increasing sequence, starting with 2, such that no two terms (possibly identical) sum to a Fibonacci number.

2, 5, 7, 9, 10, 13, 15, 18, 20, 22, 23, 26, 28, 30, 31, 34, 36, 38, 39, 41, 43, 44, 47, 49, 52, 54, 56, 57, 60, 62, 64, 65, 68, 70, 73, 75, 77, 78, 81, 83, 85, 86, 89, 91, 93, 94, 96, 98, 99, 102, 104, 107, 109, 111, 112, 115, 117, 119, 120, 123, 125, 127, 128

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..63.

Example

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

Crossrefs

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.

Sequence in context: A360411 A181713 A047482 * A174272 A062288 A077059

Adjacent sequences: A367488 A367489 A367490 * A367492 A367493 A367494

Keyword

nonn

Author

Jeffrey Shallit, Nov 20 2023

Status

approved