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A038556
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Periodic derivative of n.
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4
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0, 0, 3, 0, 5, 6, 3, 0, 9, 10, 15, 12, 5, 6, 3, 0, 17, 18, 23, 20, 29, 30, 27, 24, 9, 10, 15, 12, 5, 6, 3, 0, 33, 34, 39, 36, 45, 46, 43, 40, 57, 58, 63, 60, 53, 54, 51, 48, 17, 18, 23, 20, 29, 30, 27, 24, 9, 10, 15, 12, 5, 6, 3, 0, 65, 66, 71, 68, 77, 78, 75, 72, 89, 90, 95, 92, 85
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Every term is an evil number (A001969) and every evil number occurs an infinite number of times in this sequence. Observe self-similarity in the graph of the sequence. - T. D. Noe, Jun 22 2007
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REFERENCES
| Simmons, G. J. The structure of the differentiation digraphs of binary sequences. Ars Combin. 35 (1993), A, 71-88. Math. Rev. 95f:05052.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..4096
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FORMULA
| If n=b_k b_{k-1} ... b_0 in base 2, a(n) is number with binary expansion (b_k+b_{k-1}) (b_{k-1}+b_{k-2}) ... (b_1+b_0) (b_0+b_{k}). Also n XOR (n rotate 1).
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EXAMPLE
| 11=1011->1100 so a(11)=12.
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CROSSREFS
| Cf. A038554, A038557.
Sequence in context: A181840 A198432 A102391 * A193508 A052483 A019915
Adjacent sequences: A038553 A038554 A038555 * A038557 A038558 A038559
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Apr 08 2001
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