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A237436 Least prime p > prime(n+1) such that p is a square mod the first n odd primes 3, 5, 7, 11, ..., prime(n+1).

%I A237436 #4 Feb 15 2014 13:52:09
%S A237436 7,19,79,331,751,1171,7459,10651,18379,78439,78439,399499,644869,
%T A237436 1427911,1427911,4355311,5715319,43030381,43030381,163384621
%N A237436 Least prime p > prime(n+1) such that p is a square mod the first n odd primes 3, 5, 7, 11, ..., prime(n+1).
%C A237436 Least prime p > prime(n+1) such that p is a quadratic residue mod the first n odd primes 3, 5, 7, 11, ..., prime(n+1).
%C A237436 Least odd prime p such that the Legendre symbol (p|q) = 1 for q = 3, 5, 7, 11, ..., prime(n+1).
%H A237436 Wikipedia, <a href="https://en.wikipedia.org/wiki/Legendre_symbol">Legendre symbol</a>
%H A237436 Wikipedia, <a href="https://en.wikipedia.org/wiki/Quadratic_residue">Quadratic residue</a>
%F A237436 a(n) = a(n+1) if and only if Legendre (a(n)|prime(n+2)) = 1.
%F A237436 a(n) <= A096636(n).
%F A237436 a(n) < A096636(n) if and only if a(n) = a(n+1).
%F A237436 a(n) = A096636(n) if and only if Legendre (a(n)|prime(n+2)) = -1.
%e A237436 Let f(p) = list of Legendre (p|q) for q = 3, 5, 7, 11, 13, 17, 19, 23, ...
%e A237436 Then f(p) is
%e A237436 p=3: 0, -1, -1, 1, 1, -1, -1, 1, ...
%e A237436 p=5: -1, 0, -1, 1, -1, -1, 1, -1, ...
%e A237436 p=7: 1, -1, 0, -1, -1, -1, 1, -1, ...
%e A237436 p=11: -1, 1, 1, 0, -1, -1, 1, -1, ...
%e A237436 p=13: 1, -1, -1, -1, 0, 1, -1, 1, ...
%e A237436 p=17: -1, -1, -1, -1, 1, 0, 1, -1, ...
%e A237436 p=19: 1, 1, -1, -1, -1, 1, 0, -1, ...
%e A237436 f(7) is the first list that begins with 1, so a(1) = 7.
%e A237436 f(19) is the first list that begins with 1, 1, so a(2) = 19.
%t A237436 Table[p = Prime[n+2]; While[Length[Select[Prime[Range[2, n + 1]], JacobiSymbol[p, #] == 1 &]] < n, p = NextPrime[p]]; p, {n, 1, 18}]
%Y A237436 Cf. A222756 (p and q switched), A237437.
%K A237436 nonn
%O A237436 1,1
%A A237436 _Jonathan Sondow_, Feb 15 2014