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%I A232056 #26 Feb 15 2021 03:44:15
%S A232056 9,18,23,37,51
%N A232056 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 A232056 In most cases S(24*(3*k+1)) == 8*(3*k+1) (mod 24*(3*k+1)).
%t A232056 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 A232056 Cf. A230308, A230309, A230310, A232057.
%K A232056 nonn,more,hard
%O A232056 1,1
%A A232056 _José María Grau Ribas_, Nov 17 2013

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