A393608 - OEIS

A393608

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

%I #11 Mar 03 2026 04:52:39

%S 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,

%T 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,

%U 1,3,1,3,5,2,7,5,3,2,1,1,3,4,5,5,1,4,1,7,5,3,2

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

%C Limiting row is A000040.

%e Corner:

%e 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

%e 2 0 2 1 2 1 2 1 2 2 1 1 2 1 2 2

%e 2 3 1 3 3 1 1 3 3 1 3 1 1 3 3 1

%e 2 3 0 2 1 3 2 4 3 4 1 2 1 3 2 3

%e 2 3 5 1 5 1 5 1 5 5 1 1 5 1 5 5

%e 2 3 5 0 4 6 3 5 2 1 3 2 6 1 5 4

%e 2 3 5 7 3 5 1 3 7 5 7 5 1 3 7 5

%e 2 3 5 7 2 4 8 1 5 2 4 1 5 7 2 8

%e 2 3 5 7 1 3 7 9 3 9 1 7 1 3 7 3

%e Counting the top row as row 2, row 7 gives primes (mod 7) = (2, 3, 5, 0, 4, 6, 3, 5, ...).

%t t = Table[Mod[Prime[k], n], {n, 2, 40}, {k, 1, 40}];

%t Grid[t] (* array *)

%t v[n_, k_] := t[[n]][[k]];

%t Table[v[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* sequence *)

%Y Cf. A000040.

%K nonn,tabl

%O 2,3

%A _Clark Kimberling_, Feb 24 2026

%E More terms from _Michel Marcus_, Mar 03 2026