A393608 Rectangular array R read by descending antidiagonals: R(n,k) = prime(k) mod n, for n>=2.

0, 1, 2, 1, 0, 2, 1, 2, 3, 2, 1, 1, 1, 3, 2, 1, 2, 3, 0, 3, 2, 1, 1, 3, 2, 5, 3, 2, 1, 2, 1, 1, 1, 5, 3, 2, 1, 1, 1, 3, 5, 0, 5, 3, 2, 1, 2, 3, 2, 1, 4, 7, 5, 3, 2, 1, 2, 3, 4, 5, 6, 3, 7, 5, 3, 2, 1, 1, 1, 3, 1, 3, 5, 2, 7, 5, 3, 2, 1, 1, 3, 4, 5, 5, 1, 4, 1, 7, 5, 3, 2

Offset

2,3

Comments

Limiting row is A000040.

Links

Table of n, a(n) for n=2..92.

Example

Corner:
   0    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1
   2    0    2    1    2    1    2    1    2    2    1    1    2    1    2    2
   2    3    1    3    3    1    1    3    3    1    3    1    1    3    3    1
   2    3    0    2    1    3    2    4    3    4    1    2    1    3    2    3
   2    3    5    1    5    1    5    1    5    5    1    1    5    1    5    5
   2    3    5    0    4    6    3    5    2    1    3    2    6    1    5    4
   2    3    5    7    3    5    1    3    7    5    7    5    1    3    7    5
   2    3    5    7    2    4    8    1    5    2    4    1    5    7    2    8
   2    3    5    7    1    3    7    9    3    9    1    7    1    3    7    3
Counting the top row as row 2, row 7 gives primes (mod 7) = (2, 3, 5, 0, 4, 6, 3, 5, ...).

Mathematica

t = Table[Mod[Prime[k], n], {n, 2, 40}, {k, 1, 40}];
Grid[t]  (* array *)
v[n_, k_] := t[[n]][[k]];
Table[v[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten  (* sequence *)

Crossrefs

Cf. A000040.

Sequence in context: A180430 A246369 A036261 * A140575 A091917 A391262

Adjacent sequences: A393605 A393606 A393607 * A393609 A393610 A393611

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 24 2026

Extensions

More terms from Michel Marcus, Mar 03 2026

Status

approved