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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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6
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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
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OFFSET
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1,2
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COMMENTS
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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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R. K. Guy, Unsolved Problems in Number Theory, E38.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000
P. Alles, On a Conjecture of J. Pelikan, J. Comb. Th. A 60 (1992) 312-313.
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 ] ] & ]
(* Second program: *)
(Select[Range[1, 999, 2], OddQ[MultiplicativeOrder[2, #]]&] + 1)/2 (* Jean-François Alcover, Dec 20 2017 *)
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PROG
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(PARI) is(n)=znorder(Mod(2, 2*n-1))%2 \\ Charles R Greathouse IV, Jun 24 2015
(PARI) A000265(n)=n>>valuation(n, 2)
is(n)=Mod(2, 2*n-1)^A000265(eulerphi(2*n-1))==1 \\ Charles R Greathouse IV, Jun 24 2015
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CROSSREFS
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a(n) = (A036259(n) + 1)/2.
Sequence in context: A310567 A310568 A257692 * A328849 A261958 A057962
Adjacent sequences: A053003 A053004 A053005 * 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
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EXTENSIONS
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More terms from John W. Layman, Feb 21 2000
Additional information from Dean Hickerson, May 25 2001
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STATUS
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approved
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