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Search: id:A053006
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| A053006 |
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Values of n for which there exist d(1),...,d(n), each in {0,1}, such that Sum[d(i)d(i+k),i=1,n-k] is odd for all k=0,...,n-1. |
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+0
4
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| 1, 4, 12, 16, 24, 25, 36, 37, 40, 45, 52, 64, 76, 81, 84, 96, 100, 109, 112, 117, 120, 132, 136, 156, 165, 169, 172, 180, 184, 192, 216, 220, 232, 240, 244, 249, 252, 256, 265, 277, 300, 301, 304, 312, 316, 324, 357, 360, 361, 364, 372, 376, 412, 420, 432
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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n is in the sequence if and only if the multiplicative order of 2 (mod 2n-1) is odd.
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REFERENCES
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P. Alles, On a Conjecture of J. Pelikan, J. Comb. Th. A 60 (1992) 312-313
R. K. Guy, Unsolved Problems in Number Theory, E38.
N. F. J. Inglis and J. D. A. Wiseman, Very odd sequences, J. Comb. Th. A 71 (1995) 89-96.
F. J. MacWilliams and A. M. Odlyzko, Pelikan's conjecture and cyclotomic cosets, J. Comb. Th. A 22 (1977) 110-114.
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MATHEMATICA
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o2[ m_ ] := Module[ {e, t}, For[ e = 1; t = 2, Mod[ t-1, m ] >0, e++, t = Mod[ 2t, m ] ]; e ]; Select[ Range[ 1, 500 ], OddQ[ o2[ 2#-1 ] ] & ]
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CROSSREFS
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a(n) = (A036259(n) + 1)/2
Sequence in context: A077770 A108269 A081523 this_sequence A057962 A073687 A090818
Adjacent sequences: A053003 A053004 A053005 this_sequence A053007 A053008 A053009
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from John W. Layman (layman(AT)math.vt.edu), Feb 21 2000. Additional information from Dean Hickerson (dean.hickerson(AT)yahoo.com), May 25 2001
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