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A001986 Let p = n-th odd prime. Then a(n) = least prime congruent to 3 modulo 8 such that Legendre(-a(n), q) = -1 for all odd primes q <= p.
(Formerly M5073 N2195)
5
19, 43, 43, 67, 67, 163, 163, 163, 163, 163, 163, 222643, 1333963, 1333963, 2404147, 2404147, 20950603, 51599563, 51599563, 96295483, 96295483, 146161723, 1408126003, 3341091163, 3341091163, 3341091163, 52947440683 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers so far are all 19 mod 24. - Ralf Stephan, Jul 07 2003

REFERENCES

M. J. Jacobson, Jr., Computational Techniques in Quadratic Fields, Master's thesis, University of Manitoba, Winnipeg, Manitoba, 1995.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..27.

Michael John Jacobson Jr. and Hugh C. Williams, New quadratic polynomials with high densities of prime values, Math. Comp. 72 (2003), 499-519.

D. H. Lehmer, E. Lehmer and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp., 24 (1970), 433-451.

D. H. Lehmer, E. Lehmer and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp., 24 (1970), 433-451 [Annotated scanned copy]

PROG

isok(p, oddpn) = {forprime(q=3, oddpn, if (kronecker(-p, q) != -1, return (0)); ); return (1); }

a(n) = {my(oddpn = prime(n+1)); forprime(p=3, , if ((p%8) == 3, if (isok(p, oddpn), return (p)); ); ); } \\ Michel Marcus, Oct 17 2017

CROSSREFS

Cf. A001987, A094841-A094845, etc.

Sequence in context: A139580 A156897 A094841 * A270123 A139811 A095101

Adjacent sequences:  A001983 A001984 A001985 * A001987 A001988 A001989

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Revised Jun 14 2004

STATUS

approved

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Last modified October 20 17:24 EDT 2018. Contains 316392 sequences. (Running on oeis4.)