A331103 - OEIS

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.

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

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OFFSET

1,5

COMMENTS

Row n is a permutation of {0, 1, ..., A045326(n)-1}.

LINKS

Alois P. Heinz, Rows n = 1..75, flattened

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

Adjacent sequences: A331100 A331101 A331102 * A331104 A331105 A331106

KEYWORD

nonn,look,tabf

AUTHOR

Alois P. Heinz, Jan 09 2020

STATUS

approved