%I #16 Aug 15 2022 08:35:12
%S 1,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,2,0,1,0,0,
%T 0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,2,0,1,0,0,0,0,0,1,
%U 0,0,0,2,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,2,0,1,0,0,0,0,0,1
%N Values of k associated with A060395.
%C a(2n) = 0 for n >= 1. a(3n) = 0 for n >= 1. a(6n+1) = 1 for n >= 0. - _Nathaniel Johnston_, Apr 30 2011
%H 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.
%t a[n_] := Switch[n, 0, 1, 1, 1, _, 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, 1]]]];
%t Table[a[n], {n, 0, 101}] (* _Jean-François Alcover_, Aug 15 2022 *)
%K nonn,easy
%O 0,30
%A _N. J. A. Sloane_, Apr 04 2001
%E Name corrected and a(15)-a(97) from _Nathaniel Johnston_, Apr 30 2011