The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A060392 Let f(m) = smallest prime that divides k^2 + k + m for k = 0,1,2,...; sequence gives smallest m >= 0 such that f(m) is the n-th prime. 5
 0, 1, 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 1,3 COMMENTS Chris Nash (see the Prime Puzzles link) has shown that such an m always exists. For n>1, least odd number d such that the Legendre symbol (1-4d/prime(k)) = -1 for k = 2,...,n, but not for n+1. - 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 Table of n, a(n) for n=1..30. 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 Eric Weisstein's World of Mathematics, Prime-Generating Polynomial EXAMPLE k^2 + k takes the values 0, 2, 6, 12, ... for k = 0,1,2,...; the smallest prime divisor of these numbers is 2, so f(0) = 2. MATHEMATICA nn=20; a=Table[0, {nn}]; d=-1; While[Length[Select[a, # == 0&]] != 1, d=d+2; i=2; While[JacobiSymbol[1-4d, Prime[i]]==-1, i++ ]; If[i<=nn && a[[i]]==0, a[[i]]=d]]; a (* corrected by Jean-François Alcover, Feb 06 2019 *) PROG (PARI) lista(nn) = {va = vector(nn); d = -1; while (#select(x->(x==0), va) != 1, d += 2; i = 2; while(kronecker(1-4*d, prime(i)) == -1, i++); if ((i <= nn) && (va[i] == 0), va[i] = d); ); va; } \\ Michel Marcus, Feb 05 2019 CROSSREFS Cf. A060380, A060393-A060398. A060394 gives associated values of k. Sequence in context: A299715 A000872 A307406 * A196160 A136088 A141890 Adjacent sequences: A060389 A060390 A060391 * A060393 A060394 A060395 KEYWORD nice,nonn AUTHOR Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Apr 03 2001 EXTENSIONS Corrected by T. D. Noe, Apr 19 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 21 11:30 EDT 2024. Contains 372736 sequences. (Running on oeis4.)