A112304 - OEIS

A112304

Least number whose least prime quadratic nonresidue is prime(n).

2, 7, 19, 46, 214, 394, 1114, 3994, 3826, 13666, 83554, 22234, 189814, 644869, 1387786, 1427911, 4355311, 5715319, 12807391, 43030381, 64320754, 133826599, 452980999

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OFFSET

2,1

COMMENTS

In terms of the Legendre symbol (a|p), this sequence can be described as the least number k such that (k|prime(n))=-1 and (k|prime(i))=1 for i=2,..,n-1. Note that a(n) <= A096636(n).

LINKS

Table of n, a(n) for n=2..24.

MATHEMATICA

nn=23; a=Table[0, {nn}]; n=0; done=False; While[ !done, n++; i=2; While[i<nn+2 && JacobiSymbol[n, Prime[i]]==1, i++ ]; If[i>=2 && i<=nn+2 && JacobiSymbol[n, Prime[i]]==-1 && a[[i-1]]==0, a[[i-1]]=n; done=(Times@@a>0)]]; a

CROSSREFS

Cf. A096636 (Smallest prime whose least prime quadratic non-residue is prime(n).).

Sequence in context: A078842 A110299 A209400 * A006589 A238914 A227946

Adjacent sequences: A112301 A112302 A112303 * A112305 A112306 A112307

KEYWORD

nonn

AUTHOR

T. D. Noe, Sep 02 2005

STATUS

approved