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A094847 Let p = n-th odd prime. Then a(n) = least positive integer congruent to 5 modulo 8 such that Legendre(a(n), q) = -1 for all odd primes q <= p. 5
5, 53, 173, 173, 293, 437, 9173, 9173, 24653, 74093, 74093, 74093, 170957, 214037, 214037, 214037, 2004917, 44401013, 71148173, 154554077, 154554077, 163520117, 163520117, 163520117, 261153653, 261153653, 1728061733 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
With an initial a(0) = 5, a(n) is the least fundamental discriminant D > 1 such that the first n + 1 primes are inert in the real quadratic field with discriminant D. See A094841 for the imaginary quadratic field case. - Jianing Song, Feb 15 2019
All terms are congruent to 5 mod 24. - Jianing Song, Feb 17 2019
LINKS
Michael John Jacobson, Jr., Computational Techniques in Quadratic Fields, Master's thesis, University of Manitoba, Winnipeg, Manitoba, 1995.
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.
PROG
(PARI) isok(m, oddpn) = {forprime(q=3, oddpn, if (kronecker(m, q) != -1, return (0)); ); return (1); }
a(n) = {oddpn = prime(n+1); m = 5; while(! isok(m, oddpn), m += 8); m; } \\ Michel Marcus, Oct 17 2017
CROSSREFS
Cf. A094841 (the imaginary quadratic field case), A094842, A094843, A094844.
See A001992, A094851, A094852, A094853 for the case where the terms are restricted to the primes.
Sequence in context: A163580 A075540 A006562 * A001992 A139899 A212820
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 14 2004
STATUS
approved

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Last modified June 23 22:09 EDT 2024. Contains 373661 sequences. (Running on oeis4.)