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

0,1

Comments

Bisection of A060395.

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.

Formula

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A113965 A162277 A365512 * A352351 A359421 A014780

Adjacent sequences: A060394 A060395 A060396 * A060398 A060399 A060400

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Apr 04 2001

Extensions

More terms from Matthew Conroy, Apr 18 2001

Status

approved