Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #26 Feb 15 2021 03:44:15
%S 9,18,23,37,51
%N Numbers k such that S(24*(3*k+1)) !== 8*(3*k+1) (mod 24*(3*k+1)) where S(j) := Sum_{a=0..j-1, b=0..j-1} (a+b*i)^j and i is the imaginary unit; i.e., A230309(3*k+1) != 8*(3*k+1).
%C In most cases S(24*(3*k+1)) == 8*(3*k+1) (mod 24*(3*k+1)).
%t fu[n_] := fu[n] = Mod[Sum[PowerMod[i + j I, n, n], {i, 0, n - 1}, {j, 0, n - 1}], n]; Select[Range[50], ! fu[24*(3 # +1)] == 8*(3 # +1) &]
%Y Cf. A230308, A230309, A230310, A232057.
%K nonn,more,hard
%O 1,1
%A _José María Grau Ribas_, Nov 17 2013