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Search: id:A165418
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| A165418 |
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a(1) = 1. For n >=2, a(n) = sum a(k), where k is over the distinct values of the substrings in binary n, and where 1 <= k < n. |
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+0
2
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| 1, 1, 1, 2, 2, 3, 2, 4, 4, 4, 5, 8, 8, 8, 4, 8, 8, 8, 9, 10, 8, 13, 12, 20, 20, 20, 21, 26, 26, 20, 8, 16, 16, 16, 17, 16, 18, 21, 20, 24, 24, 16, 22, 36, 34, 35, 28, 48, 48, 48, 49, 52, 48, 55, 56, 76, 76, 76, 78, 76, 76, 48, 16, 32, 32, 32, 33, 32, 34, 37, 36, 36, 32, 40, 42, 50, 52
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OFFSET
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1,4
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COMMENT
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The distinct positive values of the substrings of binary n is row n of table A165416.
a(2^n) = 2^(n-1), for all n >=1.
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EXAMPLE
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9 in binary is 1001. The distinct positive integers that occur as substrings in binary 9 are 1, 2 (10 in binary), 4 (100 in binary), and 9 (1001 in binary). So a(9) = a(1)+a(2)+a(4) = 1 + 1 + 2 = 4.
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CROSSREFS
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A165416, A165417
Sequence in context: A066589 A007897 A106289 this_sequence A048620 A165419 A117660
Adjacent sequences: A165415 A165416 A165417 this_sequence A165419 A165420 A165421
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KEYWORD
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base,nonn,new
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Sep 17 2009
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EXTENSIONS
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More terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Nov 19 2009
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