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).

9, 18, 23, 37, 51

Offset: 1

Author

José María Grau Ribas, Nov 17 2013

Keywords

• nonn
• more
• hard

Comments

In most cases S(24*(3*k+1)) == 8*(3*k+1) (mod 24*(3*k+1)).

Crossrefs

Cf. A230308, A230309, A230310, A232057.

Programs

Mathematica

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) &]