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Search: id:A086342
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| A086342 |
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Smallest number of 1's in binary expansion of any positive multiple of n. |
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+0
2
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| 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 2, 3, 4, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 3, 2, 4, 5, 1, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 2, 2, 4, 3, 3, 2, 3, 2, 4, 2, 2, 2, 3, 3, 2, 2, 2, 4, 2, 5, 6, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 4, 2, 3, 3, 3, 2, 2, 2, 2, 3, 4, 2, 3, 2, 4, 4, 3, 3, 5, 3, 3, 2, 2, 3, 2, 2, 2, 4, 3, 2
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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If n is a power of 2 then a(n)=1. All other positive n have a(n)>1. a(n)=2 precisely in cases where some multiple of n is a factor of 2^q+1 for some q.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..10000
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EXAMPLE
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a(n)=2 for n=53, 59, 61, 67, 81, 97 and 101 because n divides 2^k+1 for k=26, 29, 30, 33, 27, 24 and 50, respectively. - T. D. Noe, Jul 22 2008
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CROSSREFS
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Cf. A005360 (flimsy numbers), A125121 (sturdy numbers), A143069 (least multiple)
Sequence in context: A037194 A111630 A106140 this_sequence A124736 A144016 A104232
Adjacent sequences: A086339 A086340 A086341 this_sequence A086343 A086344 A086345
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KEYWORD
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base,nonn
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AUTHOR
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Sean A. Irvine (sairvin(AT)xtra.co.nz), Sep 02 2003
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 21 2005
Corrected by T. D. Noe, Jul 22 2008
An incorrect Mma program was deleted Aug 01 2008
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