

A014556


Euler's "Lucky" numbers: n such that m^2m+n is prime for m=0..n1.


11




OFFSET

1,1


COMMENTS

Same as n such that 4n1 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, PrimeGenerating 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}] (* JeanFrançois Alcover, Jul 16 2012, after M. F. Hasler *)


PROG

(PARI) is(n)=n>1 && qfbclassno(14*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



