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A270271
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Odd numbers n such that for every k >= 1, n*2^k + 1 has a divisor in the set {3, 5, 17, 257, 641, 65537, 6700417}.
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1
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201446503145165177, 1007236913771681629, 1697906240793858917, 2331023822106839599, 2935363331541925531, 3367034409844073483, 3914042604075779837, 4863495246870308311, 5036162578625852633, 5590196669446332863, 6705290764721718679, 7284449444083822547
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OFFSET
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1,1
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REFERENCES
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M. Krizek, F. Luca, L. Somer, 17 Lectures on Fermat Numbers: From Number Theory to Geometry, CMS Books in Mathematics, vol. 9, Springer-Verlag, New York, 2001, pp. 72-73.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).
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FORMULA
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a(n) = a(n-64) + 2*(2^64-1) for n > 64.
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PROG
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(Magma) lst:=[]; e:=2^64; P:=PrimeDivisors(e-1); C:=[1, 1, 1, 1, 1, 1, 33]; Pr:=&*[P[i]: i in [1..#P]]; S:=CRT([Modexp(2, C[i], P[i]): i in [1..#C]], P); for t in [1..33] do a:=S+Pr; g:=Gcd(a, e); S:=Floor(a/g); Append(~lst, S); end for; Sort(lst)[1..12];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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