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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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11
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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.
F. Le Lionnais, Les Nombres Remarquables. Paris: Hermann, pp. 88 and 144, 1983.
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LINKS
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Table of n, a(n) for n=1..6.
Eric Weisstein's World of Mathematics, Lucky Number of Euler
Eric Weisstein's World of Mathematics, Prime-Generating Polynomial
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FORMULA
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a(n)=(A003173(n+3)+1)/4. [From M. F. Hasler, Nov 03 2008]
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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 *)
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PROG
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(PARI) is(n)=n>1 && qfbclassno(1-4*n)==1 \\ Charles R Greathouse IV, Jan 29 2013
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CROSSREFS
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Cf. A000926, A003173, A092749, A117530, A117531.
Sequence in context: A079370 A014210 A203074 * A062737 A085613 A082605
Adjacent sequences: A014553 A014554 A014555 * A014557 A014558 A014559
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KEYWORD
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nonn,fini,full,nice
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AUTHOR
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Eric W. Weisstein
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STATUS
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approved
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