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 A096636 Smallest prime p > prime(n+2) such that p is a quadratic residue mod the first n odd primes 3, 5, 7, 11, ..., prime(n+1), and p is a quadratic non-residue mod prime(n+2). 6
 5, 7, 19, 79, 331, 751, 1171, 7459, 10651, 18379, 90931, 78439, 399499, 644869, 2631511, 1427911, 4355311, 5715319, 49196359, 43030381, 163384621, 249623581, 452980999, 1272463669, 505313251 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Same as smallest prime p with property that the Legendre symbol (p|q) = 1 for the first n odd primes q = prime(k+1), k = 1, 2, ..., n, and (p|q) = -1 for q = prime(n+2). - T. D. Noe, Mar 06 2013 LINKS EXAMPLE Let f(p) = list of Legendre(p|q) for q = 3,5,7,11,13,... Then f(3), f(5), f(7), f(11), ... are: p=3: 0, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, ... p=5: -1, 0, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, ... p=7: 1, -1, 0, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, ... p=11: -1, 1, 1, 0, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, ... p=13: 1, -1, -1, -1, 0, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, ... p=17: -1, -1, -1, -1, 1, 0, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, ... p=19: 1, 1, -1, -1, -1, 1, 0, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, ... p=5 is the first list that begins with -1, so a(0) = 5, p=7 is the first list that begins 1, -1, so a(1) = 7, p=19 is the first list that begins 1, 1, -1, so a(2) = 19. MATHEMATICA f[n_] := Block[{k = 2}, While[ JacobiSymbol[n, Prime[k]] == 1, k++ ]; Prime[k]]; t = Table[0, {50}]; Do[p = Prime[n]; a = f[p]; If[ t[[ PrimePi[a]]] == 0, t[[ PrimePi[a]]] = p; Print[ PrimePi[a], " = ", p]], {n, 10^9}] CROSSREFS Cf. A094929, A222756 (p and q switched). See also A096637, A096638, A096639, A096640. - Jonathan Sondow, Mar 07 2013 Sequence in context: A045447 A159048 A171131 * A101588 A062654 A130729 Adjacent sequences:  A096633 A096634 A096635 * A096637 A096638 A096639 KEYWORD nonn AUTHOR Robert G. Wilson v, Jun 24 2004 EXTENSIONS Better definition from T. D. Noe, Mar 06 2013 Entry revised by N. J. A. Sloane, Mar 06 2013 Simpler definition from Jonathan Sondow, Mar 06 2013 STATUS approved

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