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Search: id:A101933
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| A101933 |
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Concatenate the first n positive integers written in binary (with each integer written so the most significant 1 is on the left and the concatenated string is from left to right, A030302). a(n) is the number of times n written in binary appears disjointedly in the concatenated string. |
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+0
1
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| 1, 1, 2, 1, 2, 3, 3, 1, 2, 1, 4, 3, 4, 5, 4, 1, 2, 2, 3, 2, 2, 1, 6, 3, 4, 4, 6, 6, 5, 7, 5, 1, 2, 2, 3, 1, 4, 3, 4, 2, 4, 2, 5, 2, 3, 4, 8, 3, 4, 5, 5, 4, 6, 4, 8, 6, 6, 6, 7, 9, 6, 9, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 2, 3, 5, 2, 6, 4, 5, 2, 4, 3, 6, 3, 3, 3, 7, 2, 5, 3, 5, 3, 7, 5, 10, 3, 4, 5, 5, 4, 7, 5, 7, 4, 6
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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First occurrence of n: 1, 3, 6, 11, 14, 23, 30, 47, 60, 95, 126, 124, 223, 248, 252, 447, 863, 504, 895, 1008, 1020, 1016, 1919, 2044, 2032, 2040, 3839, 7159, 7871, 4080, 7679, 15855, 8160, 8184, 8176, 15839, ??, 16376, 16352, 16368, ..., to a limit of 25000.
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LINKS
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Diana Mecum & Robert G. Wilson v, Table of n, a(n) for n = 1..10000.
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EXAMPLE
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a(21) = 2 because 21_10 = 10101_2 and that appears in
1101110010111011110001001101010111100110111101111100001000110010100111010010101_2
three times but only two times which do not overlap.
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MATHEMATICA
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a[n_] := StringCount[ ToString@ FromDigits@ Flatten@ IntegerDigits[ Range@n, 2], ToString@ FromDigits@ IntegerDigits[n, 2], Overlaps -> False]; Array[a, 105]
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CROSSREFS
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Cf. A007088, A030190, A030302, A058935, A047778. Differs from A117127 at positions in A141439.
Sequence in context: A077876 A095056 A140575 this_sequence A117127 A136624 A033763
Adjacent sequences: A101930 A101931 A101932 this_sequence A101934 A101935 A101936
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KEYWORD
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base,easy,nonn
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AUTHOR
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Diana Mecum (diana.mecum(AT)gmail.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 31 2008
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