A110962 Fractalization of A025480, zero-based version of Kimberling's paraphrases sequence.

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

Offset: 0

Author

Alexandre Wajnberg, Sep 26 2005

Keywords

• base
• easy
• nonn

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 sequence of Kimberling's paraphrases 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

Crossrefs

Cf. A000265, A003602, A025480, A089309, A103391, A110812, A110779, A110766.

One less than A110963 (note also the different starting offsets).

Programs

PARI

A025480(n) = (n>>valuation(n*2+2, 2));
A110962(n) = if(!(n%2), A025480(n/2), A110962((n-1)/2)); \\ Antti Karttunen, Apr 18 2022

PARI

a(n) = n++; n>>=valuation(n, 2); n>>valuation(2*n+2, 2); \\ Ruud H.G. van Tol, Jun 23 2024

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.

Extensions

Entry edited and more terms added by Antti Karttunen, Apr 18 2022