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A331103
T(n,k) = -(-1)^k*k^2 mod p, where p is the n-th prime congruent to 2 or 3 mod 4; triangle T(n,k), n>=1, 0<=k<=p-1, read by rows.
2
0, 1, 0, 1, 2, 0, 1, 3, 2, 5, 4, 6, 0, 1, 7, 9, 6, 3, 8, 5, 2, 4, 10, 0, 1, 15, 9, 3, 6, 2, 11, 12, 5, 14, 7, 8, 17, 13, 16, 10, 4, 18, 0, 1, 19, 9, 7, 2, 10, 3, 5, 12, 15, 6, 17, 8, 11, 18, 20, 13, 21, 16, 14, 4, 22, 0, 1, 27, 9, 15, 25, 26, 18, 29, 19, 24
OFFSET
1,5
COMMENTS
Row n is a permutation of {0, 1, ..., A045326(n)-1}.
LINKS
EXAMPLE
Triangle T(n,k) begins:
0, 1;
0, 1, 2;
0, 1, 3, 2, 5, 4, 6;
0, 1, 7, 9, 6, 3, 8, 5, 2, 4, 10;
0, 1, 15, 9, 3, 6, 2, 11, 12, 5, 14, 7, 8, 17, 13, 16, 10, 4, 18;
...
MAPLE
b:= proc(n) option remember; local p;
p:= 1+`if`(n=1, 1, b(n-1));
while irem(p, 4)<2 do p:= nextprime(p) od; p
end:
T:= n-> (p-> seq(modp(-(-1)^k*k^2, p), k=0..p-1))(b(n)):
seq(T(n), n=1..8);
MATHEMATICA
b[n_] := b[n] = Module[{p}, p = 1+If[n == 1, 1, b[n-1]]; While[Mod[p, 4]<2, p = NextPrime[p]]; p];
T[n_] := With[{p = b[n]}, Table[Mod[-(-1)^k*k^2, p], {k, 0, p - 1}]];
Table[T[n], {n, 1, 8}] // Flatten (* Jean-François Alcover, Oct 29 2021, after Alois P. Heinz *)
CROSSREFS
Columns k=0-1 give: A000004, A000012.
Last elements of rows give A281664.
Row lengths give A045326.
Row sums give A000217(A281664(n)).
Cf. A331047.
Sequence in context: A097609 A266692 A077884 * A267724 A179329 A089112
KEYWORD
nonn,look,tabf
AUTHOR
Alois P. Heinz, Jan 09 2020
STATUS
approved