A287476 a(0) = a(1) = 1; a(2*n) = a(n-a(n)), a(2*n+1) = a(n-a(n)) + a(n-a(n+1)).

1, 1, 1, 2, 1, 2, 1, 2, 2, 3, 2, 3, 2, 3, 2, 4, 1, 3, 1, 3, 2, 4, 2, 5, 2, 5, 2, 5, 2, 4, 3, 5, 4, 7, 2, 3, 3, 7, 1, 4, 1, 2, 3, 6, 2, 5, 1, 5, 2, 5, 2, 7, 2, 6, 2, 7, 2, 4, 5, 7, 5, 10, 2, 7, 2, 7, 2, 7, 4, 9, 4, 8, 7, 11, 3, 6, 7, 9, 3, 4, 4, 5, 4, 5, 4, 7, 7, 9, 3, 7, 1, 3, 5, 7, 3, 8, 1, 7, 2, 7, 2

Offset: 0

Author

Ilya Gutkovskiy, May 25 2017

Keywords

• nonn

Comments

A variation on Hofstadter's Q-sequence and Stern's diatomic sequence.

Links

• Eric Weisstein's World of Mathematics, Stern's Diatomic Series
• Eric Weisstein's World of Mathematics, Hofstadter's Q-Sequence
• Index entries for sequences related to Stern's sequences
• Index entries for Hofstadter-type sequences

Crossrefs

Cf. A002487, A005185, A287475, A287477.

Programs

Mathematica

a[0] = 1; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2 - a[n/2]], a[(n - 1)/2 - a[(n - 1)/2]] + a[(n - 1)/2 - a[(n + 1)/2]]]; Table[a[n], {n, 0, 100}]