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a(n) = {my(oddpn = prime(n+1)); forprime(p=3, , if ((p%248) == 19, 3, if (isok(p, oddpn), return (p)); ); ); } \\ Michel Marcus, Oct 17 2017
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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, 52947440683, 52947440683, 193310265163
Jinyuan Wang, <a href="/A001986/b001986.txt">Table of n, a(n) for n = 1..56</a>
(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%824) == 3, 19, if (isok(p, oddpn), return (p)); ); ); } \\ Michel Marcus, Oct 17 2017
a(28)-a(30) from Jinyuan Wang, Apr 09 2020
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Also a(n) is the least prime p r congruent to 3 mod 8 such that the first n odd primes are quadratic nonresidues modulo pr. Note that p r == 3 (mod 8) implies 2 is a quadratic nonresidue modulo pr. See A001992 for the case where p r == 5 (mod 8). - Jianing Song, Feb 19 2019
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