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A014556 Euler's "Lucky" numbers: n such that m^2-m+n is prime for m=0..n-1. 15
2, 3, 5, 11, 17, 41 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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).

REFERENCES

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.

LINKS

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

FORMULA

a(n)=(A003173(n+3)+1)/4. [From M. F. Hasler, Nov 03 2008]

MATHEMATICA

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-Fran├žois Alcover, Jul 16 2012, after M. F. Hasler *)

PROG

(PARI) is(n)=n>1 && qfbclassno(1-4*n)==1 \\ Charles R Greathouse IV, Jan 29 2013

CROSSREFS

Cf. A000926, A003173, A092749, A117530, A117531.

Sequence in context: A079370 A014210 A203074 * A062737 A085613 A082605

Adjacent sequences:  A014553 A014554 A014555 * A014557 A014558 A014559

KEYWORD

nonn,fini,full,nice

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified December 8 09:03 EST 2016. Contains 278906 sequences.