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A053006 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. 6
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

n is in the sequence if and only if the multiplicative order of 2 (mod 2n-1) is odd.

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, E38.

LINKS

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.

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

a(n) = (A036259(n) + 1)/2.

Sequence in context: A310567 A310568 A257692 * A328849 A261958 A057962

Adjacent sequences: A053003 A053004 A053005 * A053007 A053008 A053009

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from John W. Layman, Feb 21 2000

Additional information from Dean Hickerson, May 25 2001

STATUS

approved

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Last modified February 7 06:02 EST 2023. Contains 360112 sequences. (Running on oeis4.)