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 A060380 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. 4
 2, 3, 5, 47, 11, 221, 17, 1217, 941, 2747, 8081, 9281, 41, 55661, 19421, 333491, 1262201, 601037, 5237651, 9063641, 12899891, 26149427, 24073871, 28537121, 352031501, 398878547, 160834691, 67374467, 146452961, 24169417397 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Chris Nash (see the Prime Puzzles link) has shown that such an m always exists. 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 REFERENCES 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 LINKS G. W. Fung and H. C. Williams, Quadratic polynomials with high density of primes, Mathematics of Computation, Vol. 55, 1990. C. Rivera, www.primepuzzles.net, Conjecture 17 EXAMPLE 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. MATHEMATICA (* This program is not convenient beyond a(24) *) a = 2; a = 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 *) CROSSREFS Cf. A060392-A060398. A060393 gives associated values of k. Sequence in context: A281252 A208223 A136371 * A062608 A041791 A322947 Adjacent sequences:  A060377 A060378 A060379 * A060381 A060382 A060383 KEYWORD hard,nice,nonn AUTHOR Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Apr 03 2001 EXTENSIONS Corrected by T. D. Noe, Apr 19 2004 STATUS approved

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Last modified May 20 23:05 EDT 2022. Contains 353886 sequences. (Running on oeis4.)