Voozh

A110962

Fractalization of A025480, zero-based version of Kimberling's paraphrase of the binary number system.

0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 1, 0, 3, 0, 0, 0, 4, 2, 2, 1, 5, 1, 1, 0, 6, 3, 3, 0, 7, 0, 0, 0, 8, 4, 4, 2, 9, 2, 2, 1, 10, 5, 5, 1, 11, 1, 1, 0, 12, 6, 6, 3, 13, 3, 3, 0, 14, 7, 7, 0, 15, 0, 0, 0, 16, 8, 8, 4, 17, 4, 4, 2, 18, 9, 9, 2, 19, 2, 2, 1, 20, 10, 10, 5, 21, 5, 5, 1, 22, 11, 11, 1, 23, 1, 1, 0, 24, 12, 12

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OFFSET

0,9

COMMENTS

Self-descriptive sequence: the terms at odd indices are the sequence itself, while the terms at even indices (the skeleton of this sequence) are the terms of A025480, which is a zero-based version of Kimberling's paraphrase sequence, A003602.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

Clark Kimberling, Fractal sequences

Index entries for sequences related to binary expansion of n

FORMULA

For even n, a(n) = A025480(n/2), for odd n, a(n) = a((n-1)/2). - Antti Karttunen, Apr 18 2022

a(2n+1) = a(4n+3) = a(n).

a(2n) = a(4n+1) = a(4n+2) = A025480(n/2).

a(4n) = a(8n+1) = a(8n+2) = n.

a(n) = A110963(1+n) - 1.

MATHEMATICA

A110962[n_] := Nest[(BitShiftRight[#, IntegerExponent[#, 2]] + 1)/2 &, n + 1, 2] - 1;