A396674 a(n) is the Fibonacci-code successor of n.

1, 2, 4, 4, 5, 8, 8, 8, 9, 10, 16, 16, 13, 16, 16, 16, 17, 18, 20, 20, 21, 32, 32, 32, 25, 26, 32, 32, 29, 32, 32, 32, 33, 34, 36, 36, 37, 40, 40, 40, 41, 42, 64, 64, 45, 64, 64, 64, 49, 50, 52, 52, 53, 64, 64, 64, 57, 58, 64, 64, 61, 64, 64, 64, 65, 66, 68, 68, 69, 72

Offset

0,2

References

Donald E. Knuth, The Art of Computer Programming, Volume 1, Fundamental Algorithms. Third Edition, Addison-Wesley, 1997. Chapter 1.2.8, exercise 34, page 86, introduces the Fibonacci number system first described by E. Zeckendorf, see answer page 495.

Donald E. Knuth, The Art of Computer Programming, Volume 4A, Combinatorial Algorithms Part 1. Pearson Education, 2011. Chapter 7.1.3, exercise 158, page 196, asks for a method to increment Fibonacci codewords with answer on page 607.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Mathematica

A396674[n_] := BitOr[n, BitAnd[#, BitNot[#+1]]] + 1 & [BitOr[n, BitShiftRight[n]]];
Array[A396674, 100, 0] (* Paolo Xausa, Jun 08 2026, after PARI *)

Prog

(PARI) a396674(x) = my(y=bitor(x, x>>1), z=bitand(y, bitneg(y+1))); bitor(x, z)+1

Crossrefs

Cf. A215026.

Sequence in context: A327625 A084824 A344710 * A184615 A151969 A261393

Adjacent sequences: A396671 A396672 A396673 * A396675 A396676 A396677

Keyword

nonn,easy

Author

Hugo Pfoertner, Jun 08 2026

Status

approved