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
Offset: 1
Examples
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; ...
Links
- Alois P. Heinz, Rows n = 1..75, flattened
Crossrefs
Programs
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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 *)
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