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A053006
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Numbers m for which there exist d(1),...,d(m), each in {0,1}, such that Sum_{i=1..m-k} d(i)*d(i+k) is odd for all k=0,...,m-1.
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7
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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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m is in the sequence if and only if the multiplicative order of 2 (mod 2m-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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FORMULA
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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) A000265(n)=n>>valuation(n, 2)
(Python)
from sympy import n_order
def A053006_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:n_order(2, (n<<1)-1)&1, count(max(startvalue, 1)))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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