A060397 Smallest prime that divides k^2 + k + 2n + 1 for k = 0,1,2,....

3, 3, 5, 3, 3, 11, 3, 3, 17, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 41, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 11, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 11, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 11, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 7, 3, 3

Offset: 0

Author

N. J. A. Sloane, Apr 04 2001

Keywords

• nonn
• easy
• nice

Comments

Bisection of A060395.

Examples

			To obtain a(3), note that x^2+x+7 takes the values 7,9,13,19,... for k=0,1,2,... and the smallest prime dividing these numbers is 3.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000
• Carlos Rivera, Conjecture 17. The Ludovicus conjecture about the Euler trinomials, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A060380, A060392-A060398. A060398 gives values of k.

Programs

Mathematica

a[n_] := Switch[n, 0, 3, , Module[{f, kmax0 = 2}, f[kmax] := f[kmax] = MinimalBy[Table[{k, FactorInteger[k^2 + k + 2 n + 1][[1, 1]]}, {k, 0, kmax}], Last, 1]; f[kmax = kmax0]; f[kmax = 2 kmax]; While[f[kmax] != f[kmax/2], kmax = 2 kmax]; f[kmax][[1, 2]]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Aug 15 2022 *)

Formula

a(n)=3 if n is equal to 0 or 1 mod 3.

Extensions

More terms from Matthew Conroy, Apr 18 2001