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Search: id:A137397
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| A137397 |
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Number of distinct palindromic subwords in the binary representation of n. |
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+0
1
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| 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Equals A070941 from a(1) to a(202) and continues a(203)=8, a(204)=a(205)=9.
Omitting "distinct" in the definition, we get 1, 2, 4, 4, 7, 7, 7, 7, 11, 11, 11, 11, 11, 11, 11, 11, 16, 16,... which apparently is build by repeating entries of A000124 in blocks of length 2,4,8,16,32..
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LINKS
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A. Glen, J. Justin, S. Widmer, L. Q. Zamboni, Palindromic Richness, arXiv:0801.1656 [math.CO]
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EXAMPLE
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For n=10 the binary representation is A007088(10)=1010, which contains the a(10)=5 palindromic substrings {}, {0}, {1}, {101}, {010}. The empty subword is always included in the count.
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CROSSREFS
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Cf. A070941.
Sequence in context: A157792 A094235 A156876 this_sequence A062571 A102515 A066063
Adjacent sequences: A137394 A137395 A137396 this_sequence A137398 A137399 A137400
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KEYWORD
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nonn
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 11 2008
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