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Search: id:A103318
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| A103318 |
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Number of solutions i in range [0,n-1] to i == 0 mod 2^(n-i). |
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+0
6
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| 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 1, 2, 2, 3, 2, 3, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 1, 2, 2, 3, 2, 3, 3, 2, 1, 2, 2, 3, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 1, 2, 2, 3
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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i=0 is always a solution.
a(n) is the number of 1's in (A103745(n) written in base 2). - Philippe DELEHAM, Apr 02 2005
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LINKS
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David Applegate, Benoit Cloitre, Philippe DELEHAM and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
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FORMULA
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a(n) = A104234(2^n - n). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Apr 21 2005
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EXAMPLE
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For n = 11 solutions are i = 0, 8 and 10. Four solutions occur for the first time at n = 2059: they are i = 0, 2048, 2056, 2058. Five solutions occur for the first time at n = 2^2059 + 2059 (see A034797).
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MAPLE
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f:= proc (n) local t1, l; t1 := 0; for l to n do if `mod`(n-l, 2^l) = 0 then t1 := t1+1 end if end do; t1 end proc;
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MATHEMATICA
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f[n_] := Block[{c = 1, k = Max[1, n - Floor[ Log[2, n] + 2]]}, While[k < n, If[ Mod[k, 2^(n - k)] == 0, c++ ]; k++ ]; c]; Table[ f[n], {n, 105}] (from Robert G. Wilson v Mar 21 2005)
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CROSSREFS
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For records see A034797. Cf. A103745.
Sequence in context: A066086 A160520 A145866 this_sequence A002321 A043530 A164995
Adjacent sequences: A103315 A103316 A103317 this_sequence A103319 A103320 A103321
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mar 21 2005
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