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A334294 Numbers k such that 70*k^2 + 70*k - 1 is prime.

%I A334294 #22 May 28 2020 03:03:09
%S A334294 1,2,3,4,5,6,7,8,9,10,11,13,14,17,20,22,23,24,26,27,29,30,31,33,34,36,
%T A334294 37,39,40,41,43,44,45,46,56,57,58,59,60,61,63,64,65,66,67,68,70,71,74,
%U A334294 76,77,78,79,80,81,82,87,88,90,93,96,97,100
%N A334294 Numbers k such that 70*k^2 + 70*k - 1 is prime.
%C A334294 Among quadratic polynomials in k of the form a*k^2 + a*k - 1 the value a=70 gives the most primes for any a in the range 1<=a<=300, at least up to k=40000. Here a and k are positive integers. Other "good" values of a are a=250, a=99, and a=19.
%H A334294 N. Boston et M. L.Greenwood, <a href="https://www.jstor.org/stable/2974555">Quadratics representing primes</a>, Amer. Math. Monthly 102:7 (1995), 595-599.
%H A334294 François Dress and Michel Olivier, <a href="https://projecteuclid.org/euclid.em/1047262355">Polynômes prenant des valeurs premières</a>, Experimental Mathematics, Volume 8, Issue 4 (1999), 319-338.
%H A334294 G. W. Fung and H. C. Williams, <a href="https://www.jstor.org/stable/2008810">Quadratic polynomials which have a high density of prime values</a>, Math. Comput. 55(191) (1990), 345-353.
%H A334294 R. A. Mollin, <a href="http://www.jstor.org/stable/2975080">Prime-Producing Quadratics</a>, The American Mathematical Monthly, Vol. 104, No. 6 (Jun. - Jul., 1997), pp. 529-544.
%e A334294 For k=1, 70*k^2 + 70*k - 1 = 70*1^2 + 70*1 - 1 = 139, which is prime, so 1 is in the sequence.
%p A334294 a:=proc(n) if isprime(70*n^2+70*n-1) then n else NULL end if end proc;
%p A334294 seq(a(n),n=1..100);
%t A334294 Select[Range@ 100, PrimeQ[70 #^2 + 70 # - 1] &] (* _Michael De Vlieger_, May 26 2020 *)
%Y A334294 Cf. A001912, A002384, A005574, A027861, A028870, A056900.
%Y A334294 Cf. A067201, A088572, A089623, A091199, A271980.
%K A334294 nonn
%O A334294 1,2
%A A334294 _James R. Buddenhagen_, Apr 21 2020