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A270271 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}. 1
201446503145165177, 1007236913771681629, 1697906240793858917, 2331023822106839599, 2935363331541925531, 3367034409844073483, 3914042604075779837, 4863495246870308311, 5036162578625852633, 5590196669446332863, 6705290764721718679, 7284449444083822547 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

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.

LINKS

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..64

Chris Caldwell, The Prime Glossary, Sierpinski number

W. Sierpiński, Sur un problème concernant les nombres k * 2^n + 1, Elem. Math., 15 (1960), pp. 63-74.

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).

FORMULA

a(n) = a(n-64) + 2*(2^64-1) for n > 64.

PROG

(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];

CROSSREFS

Cf. A257647. Subsequence of A076336.

Sequence in context: A292634 A308287 A295740 * A094676 A327760 A054213

Adjacent sequences:  A270268 A270269 A270270 * A270272 A270273 A270274

KEYWORD

nonn

AUTHOR

Arkadiusz Wesolowski, Mar 14 2016

STATUS

approved

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Last modified December 9 22:27 EST 2019. Contains 329880 sequences. (Running on oeis4.)