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A110963
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Fractalization of Kimberling's paraphrases sequence beginning with 1.
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6
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1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 1, 4, 1, 1, 1, 5, 3, 3, 2, 6, 2, 2, 1, 7, 4, 4, 1, 8, 1, 1, 1, 9, 5, 5, 3, 10, 3, 3, 2, 11, 6, 6, 2, 12, 2, 2, 1, 13, 7, 7, 4, 14, 4, 4, 1, 15, 8, 8, 1, 16, 1, 1, 1, 17, 9, 9, 5, 18, 5, 5, 3, 19, 10, 10, 3, 20, 3, 3, 2, 21, 11, 11, 6, 22, 6, 6, 2, 23, 12, 12, 2, 24, 2, 2, 1, 25, 13
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OFFSET
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1,5
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COMMENTS
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Self-descriptive sequence: terms at even indices are the sequence itself, terms at odd indices (the skeleton of this sequence) are the terms of Kimberling's paraphrases sequence (A003602) beginning with 1.
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LINKS
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FORMULA
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For n >= 0, (Start)
a(4n+1) = a(8n+2) = a(8n+3) = 1+n.
(End)
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PROG
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(PARI)
A003602(n) = (1+(n>>valuation(n, 2)))/2;
(PARI) a(n) = n>>=valuation(n, 2); 1+n>>valuation(2*n+2, 2); \\ Ruud H.G. van Tol, Jun 23 2024
(Python)
def A110963(n): return (1+(m:=n>>(~n&n-1).bit_length())>>(m+1&-m-1).bit_length())+1 # Chai Wah Wu, Jan 04 2024
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CROSSREFS
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One more than A110962 (but note the different starting offsets).
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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Entry edited, starting offset corrected (from 0 to 1), and the offsets in formulas changed accordingly, and more terms added by Antti Karttunen, Apr 03 2022
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STATUS
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approved
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