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A060395
Smallest prime that divides k^2 + k + n for k = 0, 1, 2, ....
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
OFFSET
0,1
LINKS
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
KEYWORD
nonn,easy,nice
AUTHOR
N. J. A. Sloane, Apr 04 2001
EXTENSIONS
More terms from Matthew Conroy, Apr 18 2001
STATUS
approved