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Search: id:A122953
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| A122953 |
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a(n) = number of distinct positive integers represented in binary which are substrings of binary expansion of n. |
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10
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| 1, 2, 2, 3, 3, 4, 3, 4, 4, 4, 5, 6, 6, 6, 4, 5, 5, 5, 6, 6, 5, 7, 7, 8, 8, 8, 8, 9, 9, 8, 5, 6, 6, 6, 7, 6, 7, 8, 8, 8, 8, 6, 8, 10, 9, 10, 9, 10, 10, 10, 10, 11, 10, 10, 11, 12, 12, 12, 12, 12, 12, 10, 6, 7, 7, 7, 8, 7, 8, 9, 9, 8, 7, 9, 10, 10, 11, 11, 10, 10, 10, 10, 11, 9, 7, 11, 11, 13, 13, 12
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = A078822(n) if n is of the form 2^k - 1. Otherwise, a(n) = A078822(n) - 1.
First occurrence of k: 1, 2, 4, 6, 11, 12, 22, 24, 28, 44, 52, 56, 88, 92, 112, 116, 186, 184, 220, 232, 244, 368, 376, 440, 472, ...,.
Last occurrence of k: 2^n -1.
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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Binary 1 = 1, binary 2 = 10, binary 4 = 100 and binary 9 = 1001 are all substrings of binary 9 = 1001. So a(9) = 4.
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MATHEMATICA
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f[n_] := Length@ Select[ Union[ FromDigits /@ Flatten[ Table[ Partition[ IntegerDigits[n, 2], i, 1], {i, Floor[ Log[2, n] + 1]}], 1]], # > 0 &]; Array[f, 90]
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CROSSREFS
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Cf. A078822.
Sequence in context: A066412 A117119 A139141 this_sequence A128998 A137813 A003313
Adjacent sequences: A122950 A122951 A122952 this_sequence A122954 A122955 A122956
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Oct 25 2006
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EXTENSIONS
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More terms from Robert G. Wilson v Nov 01 2006
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