A232057 -id:A232057

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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).

+10
1

9, 18, 23, 37, 51

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..5.

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) &]

CROSSREFS

Cf. A230308, A230309, A230310, A232057.

KEYWORD

nonn,more,hard

AUTHOR

José María Grau Ribas, Nov 17 2013

STATUS

approved

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