A380960 Sum of n and the n-th bit of the infinite Fibonacci word.

0, 2, 2, 3, 5, 5, 7, 7, 8, 10, 10, 11, 13, 13, 15, 15, 16, 18, 18, 20, 20, 21, 23, 23, 24, 26, 26, 28, 28, 29, 31, 31, 32, 34, 34, 36, 36, 37, 39, 39, 41, 41, 42, 44, 44, 45, 47, 47, 49, 49, 50, 52, 52, 54, 54, 55, 57, 57, 58, 60, 60, 62, 62, 63, 65, 65, 66

Offset: 0

Author

Jeffrey Shallit, Feb 09 2025

Keywords

• nonn

Comments

Also the length of the "scrambled part" of the n-th row of the Hurt-Sada array (depicted in A368050). This is the portion of the n-th row whose i-th term differs from i. See Shallit (2025), Theorem 10.

Links

• J. Shallit, The Hurt-Sada array and Zeckendorf representations, arXiv:2501.08823 [math.NT], January 15 2025.

Crossrefs

Cf. A003849, A368050.

Formula

a(n) = A003849(n) + n.