A337634 Number of numbers k <= n such that both k and k+1 are in A095096.

0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 16, 16, 16, 16, 16, 16, 16, 17

Offset

0,10

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Anton Shutov, On the Sum of Digits of the Zeckendorf Representations of Two Consecutive Numbers, The Fibonacci Quarterly, Vol. 58, No. 3 (2020), pp. 203-207.

Formula

a(n) ~ (sqrt(5)/10) * n + O(log(n)) (Shutov, 2020). - Amiram Eldar, Dec 23 2025

Mathematica

s = SequencePosition[Mod[DigitCount[Select[Range[0, 400], BitAnd[#, 2 #] == 0 &], 2, 1], 2], {0, 0}][[;; , 1]] - 1; t = Table[0, {s[[-1]] + 1}]; t[[s + 1]] = 1; Accumulate[t] (* Amiram Eldar, Feb 05 2023 *)

Crossrefs

Cf. A020899, A095096, A337287, A337288, A337289, A337290, A337635, A337636, A337637.

Sequence in context: A194235 A029120 A078428 * A316355 A055768 A349909

Adjacent sequences: A337631 A337632 A337633 * A337635 A337636 A337637

Keyword

nonn,base

Author

N. J. A. Sloane, Sep 12 2020

Extensions

Offset corrected by Amiram Eldar, Feb 05 2023

Status

approved