This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060397 #14 Aug 15 2022 08:34:37
%S A060397 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,
%T A060397 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,
%U A060397 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
%N A060397 Smallest prime that divides k^2 + k + 2n + 1 for k = 0,1,2,....
%C A060397 Bisection of A060395.
%H A060397 T. D. Noe, <a href="/A060397/b060397.txt">Table of n, a(n) for n = 0..10000</a>
%H A060397 Carlos Rivera, <a href="http://www.primepuzzles.net/conjectures/conj_017.htm">Conjecture 17. The Ludovicus conjecture about the Euler trinomials</a>, The Prime Puzzles & Problems Connection.
%F A060397 a(n)=3 if n is equal to 0 or 1 mod 3.
%e A060397 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.
%t A060397 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]]]];
%t A060397 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Aug 15 2022 *)
%Y A060397 Cf. A060380, A060392-A060398. A060398 gives values of k.
%K A060397 nonn,easy,nice
%O A060397 0,1
%A A060397 _N. J. A. Sloane_, Apr 04 2001
%E A060397 More terms from _Matthew Conroy_, Apr 18 2001