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A001992 Let p = n-th odd prime. Then a(n) = least prime congruent to 5 modulo 8 such that Legendre(a(n), q) = -1 for all odd primes q <= p.
(Formerly M4012 N1663)
4
5, 53, 173, 173, 293, 2477, 9173, 9173, 61613, 74093, 74093, 74093, 170957, 360293, 679733, 2004917, 2004917, 69009533, 138473837, 237536213, 384479933, 883597853, 1728061733, 1728061733, 1728061733, 1728061733 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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..26.

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. [There is an error in the table given in this paper.]

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

PROG

(PARI) 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) == 5, if (isok(p, oddpn), return (p)); ); ); } \\ Michel Marcus, Oct 17 2017

CROSSREFS

Cf. A094842-A094846, A094848-A094851, etc., A001986, A001987.

Sequence in context: A075540 A006562 A094847 * A139899 A212820 A094849

Adjacent sequences:  A001989 A001990 A001991 * A001993 A001994 A001995

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Corrected and extended Jun 14 2004.

STATUS

approved

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Last modified October 16 12:35 EDT 2018. Contains 316263 sequences. (Running on oeis4.)