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
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
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