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A096638 Smallest prime p == 3 mod 8 (A007520) and p > prime(n+2) such that p is a quadratic residue mod the first n odd primes 3, 5, 7, 11, ..., prime(n+1), and p is a quadratic non-residue mod prime(n+2). 2
11, 43, 19, 211, 331, 2011, 1171, 7459, 10651, 18379, 90931, 257371, 399499, 1234531, 6938779, 3574411, 14669251, 39803611, 102808099, 288710899, 322503091, 465390979, 1582819291, 2410622971, 505313251 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Same as smallest prime p == 3 mod 8 with the property that the Legendre symbol (p|q) = 1 for the first n odd primes q = prime(k+1), k = 1, 2, ..., n, and (p|q) = -1 for q = prime(n+2).

LINKS

Table of n, a(n) for n=0..24.

MATHEMATICA

f[n_] := Block[{k = 2}, While[ JacobiSymbol[n, Prime[k]] == 1, k++ ]; Prime[k]]; t = Table[0, {50}]; Do[p = Prime[n]; If[Mod[p, 8] == 3, a = f[p]; If[ t[[ PrimePi[a]]] == 0, t[[ PrimePi[a]]] = p; Print[ PrimePi[a], " = ", p]]], {n, 10^9}]; t

CROSSREFS

Cf. A096633, A096636.

Sequence in context: A050489 A156533 A228811 * A089712 A155711 A226617

Adjacent sequences:  A096635 A096636 A096637 * A096639 A096640 A096641

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jun 24 2004

EXTENSIONS

Better name from Jonathan Sondow, Mar 07 2013

STATUS

approved

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Last modified August 7 06:02 EDT 2020. Contains 336274 sequences. (Running on oeis4.)