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A094847
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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.
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5
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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