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%I #14 Feb 10 2019 17:16:48
%S 2,3,5,47,11,221,17,1217,941,2747,8081,9281,41,55661,19421,333491,
%T 1262201,601037,5237651,9063641,12899891,26149427,24073871,28537121,
%U 352031501,398878547,160834691,67374467,146452961,24169417397
%N Let f(m) = smallest prime that divides k^2 + k + m for k = 0,1,2,...; sequence gives smallest m >= 2 such that f(m) is the n-th prime, or -1 if no such m exists.
%C Chris Nash (see the Prime Puzzles link) has shown that such an m always exists.
%C For n>2, least odd number d such that the Legendre symbol (1-4d/prime(k)) = -1 for k = 2,...,n, but not for n+1. See A060392. - _T. D. Noe_, Apr 19 2004
%D R. F. Lukes, C. D. Patterson and H. C. Williams, Numerical sieving devices: their history and some applications. Nieuw Arch. Wisk. (4) 13 (1995), no. 1, 113-139. Math. Rev. 96m:11082
%H G. W. Fung and H. C. Williams, <a href="https://doi.org/10.1090/S0025-5718-1990-1023759-3">Quadratic polynomials with high density of primes</a>, Mathematics of Computation, Vol. 55, 1990.
%H C. Rivera, <a href="http://www.primepuzzles.net/conjectures/conj_017.htm">www.primepuzzles.net, Conjecture 17</a>
%e k^2 + k + 2 takes the values 2, 4, 8, 14, ... for k = 0,1,2,...; the smallest prime divisor of these numbers is 2, so f(2) = 2.
%t (* This program is not convenient beyond a(24) *) a[1] = 2; a[2] = 3; a[n_] := For[d = 1, True, d = d+2, If[And @@ (# == -1 & /@ Table[JacobiSymbol[1 - 4d, Prime[k]], {k, 2, n}]) && JacobiSymbol[1 - 4d, Prime[n+1]] != -1, Return[d]]]; Table[Print[an = a[n]]; an, {n, 1, 24}] (* _Jean-François Alcover_, Oct 14 2013, after _T. D. Noe_ *)
%Y Cf. A060392-A060398. A060393 gives associated values of k.
%K hard,nice,nonn
%O 1,1
%A Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Apr 03 2001
%E Corrected by _T. D. Noe_, Apr 19 2004
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