A297208 a(0)=0; for n >= 1, a(n) = a(n-1-A023416(n)) + A000120(n).

0, 1, 1, 3, 2, 5, 4, 7, 3, 6, 9, 9, 8, 12, 11, 15, 10, 14, 13, 13, 12, 16, 16, 20, 14, 19, 23, 23, 22, 27, 26, 31, 24, 24, 29, 34, 33, 27, 32, 37, 36, 30, 35, 40, 39, 39, 44, 44, 42, 42, 47, 46, 45, 51, 50, 56, 48, 54, 60, 59, 58, 64, 63, 69, 55, 61, 60, 66, 65, 58, 64, 70, 62, 68

Offset: 0

Author

Ctibor O. Zizka, Dec 27 2017

Keywords

• nonn
• base

Examples

			For n = 7, A023416(7) = 0, A000120(7) = 3 so a(7) = a(6) + 3 , a(6) = a(4) + 2, a(4) = a(1) + 1 , a(1) = a(0) + 1 , a(0) = 0. Thus a(7)= 0 + 1 + 1 + 2 + 3 = 7.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• B. Balamohan, A. Kuznetsov and S. Tanny, On the behavior of a variant of Hofstadter's Q-sequence, J. Integer Sequences, Vol. 10 (2007), Article 07.7.1.
• Nathaniel D. Emerson, A Family of Meta-Fibonacci Sequences Defined by Variable-Order Recursions, J. Integer Sequences, Vol. 9 (2006), Article 06.1.8.

Crossrefs

Cf. A023416, A000120.

Programs

Mathematica

a[0] = 0; a[n_] := a[n] = a[n - 1 - DigitCount[n, 2, 0]] + DigitCount[n, 2, 1]; Array[a, 100, 0] (* Amiram Eldar, Jul 20 2023 *)

PARI

a(n) = if (n==0, 0, a(n-1-#binary(n)+hammingweight(n)) + hammingweight(n)); \\ Michel Marcus, Dec 27 2017