A060395 - OEIS

A060395

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

2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 11, 2, 3, 2, 3, 2, 17, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 41, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 11

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..101.

Carlos Rivera, Conjecture 17. The Ludovicus conjecture about the Euler trinomials, The Prime Puzzles & Problems Connection.

FORMULA

a(n)=2 if n is equal to 0, 2 or 4 modulo 6; a(n)=3 if n is equal to 1 or 3 modulo 6.

EXAMPLE

To obtain a(7), 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, 2, 1, 3, _, Module[{f, kmax0 = 2}, f[kmax_] := f[kmax] = MinimalBy[Table[{k, FactorInteger[k^2 + k + n][[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, 101}] (* Jean-François Alcover, Aug 15 2022 *)

CROSSREFS

Cf. A060380, A060392-A060398. A060396 gives values of k.

Sequence in context: A342309 A112047 A112048 * A016026 A086757 A369690

Adjacent sequences: A060392 A060393 A060394 * A060396 A060397 A060398

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Apr 04 2001

EXTENSIONS

More terms from Matthew Conroy, Apr 18 2001

STATUS

approved