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A060397 Smallest prime that divides k^2 + k + 2n + 1 for k = 0,1,2,.... 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Bisection of A060395.
LINKS
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
KEYWORD
nonn,easy,nice
AUTHOR
N. J. A. Sloane, Apr 04 2001
EXTENSIONS
More terms from Matthew Conroy, Apr 18 2001
STATUS
approved

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Last modified July 23 04:43 EDT 2024. Contains 374544 sequences. (Running on oeis4.)