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A014556
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Euler's "Lucky" numbers: n such that m^2-m+n is prime for m=0..n-1.
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26
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OFFSET
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1,1
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COMMENTS
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Same as n such that 4n-1 is a Heegner number 1,2,3,7,11,19,43,67,163 (see A003173 and Conway and Guy's book).
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REFERENCES
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J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 225.
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 41, p. 16, Ellipses, Paris 2008.
I. N. Herstein and I. Kaplansky, Matters Mathematical, Chelsea, NY, 2nd. ed., 1978, see p. 38.
F. Le Lionnais, Les Nombres Remarquables. Paris: Hermann, pp. 88 and 144, 1983.
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LINKS
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FORMULA
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MATHEMATICA
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A003173 = Union[Select[-NumberFieldDiscriminant[Sqrt[-#]] & /@ Range[200], NumberFieldClassNumber[Sqrt[-#]] == 1 &] /. {4 -> 1, 8 -> 2}]; a[n_] := (A003173[[n + 4]] + 1)/4; Table[a[n], {n, 0, 5}] (* Jean-François Alcover, Jul 16 2012, after M. F. Hasler *)
Select[Range[50], AllTrue[Table[m^2-m+#, {m, 0, #-1}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 12 2017 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,fini,full,nice
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AUTHOR
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STATUS
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approved
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