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URL: https://oeis.org/A110962

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A110962
Fractalization of A025480, zero-based version of Kimberling's paraphrase of the binary number system.
3
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
0,9
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.
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;
Array[A110962, 100, 0] (* Paolo Xausa, Sep 12 2025 *)
PROG
(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
CROSSREFS
One less than A110963 (note also the different starting offsets).
Sequence in context: A301636 A238857 A253587 * A065715 A180984 A051628
KEYWORD
base,easy,nonn
AUTHOR
Alexandre Wajnberg, Sep 26 2005
EXTENSIONS
Entry edited and more terms added by Antti Karttunen, Apr 18 2022
Edited to match Kimberling's terminology by Peter Munn, Sep 11 2025
STATUS
approved