A214810 Triangle read by rows: T(n,k) (n>=1, 0 <= k <= p where p = n-th prime) = Bell(k) mod p (cf. A000110).

1, 1, 0, 1, 1, 2, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 5, 1, 3, 0, 2, 1, 1, 2, 5, 4, 8, 5, 8, 4, 5, 2, 2, 1, 1, 2, 5, 2, 0, 8, 6, 6, 9, 2, 9, 11, 2, 1, 1, 2, 5, 15, 1, 16, 10, 9, 16, 1, 15, 11, 6, 15, 11, 14, 2, 1, 1, 2, 5, 15, 14, 13, 3, 17, 0, 18, 4, 5, 7, 14, 16, 15, 1, 10, 2, 1, 1, 2, 5, 15, 6, 19, 3, 0, 10, 9, 1, 20, 1, 12, 9, 5, 6, 6, 9, 4, 16, 22, 2, 1, 1, 2, 5, 15, 23, 0

Offset: 1

Author

N. J. A. Sloane, Jul 31 2012

Keywords

• nonn
• look
• tabf

Comments

The n-th row gives Bell numbers mod prime(n) and has length prime(n)+1.

Examples

			Triangle begins:
  [1, 1, 0],
  [1, 1, 2, 2],
  [1, 1, 2, 0, 0, 2],
  [1, 1, 2, 5, 1, 3, 0, 2],
  [1, 1, 2, 5, 4, 8, 5, 8, 4, 5, 2, 2],
  [1, 1, 2, 5, 2, 0, 8, 6, 6, 9, 2, 9, 11, 2],
  [1, 1, 2, 5, 15, 1, 16, 10, 9, 16, 1, 15, 11, 6, 15, 11, 14, 2],
  [1, 1, 2, 5, 15, 14, 13, 3, 17, 0, 18, 4, 5, 7, 14, 16, 15, 1, 10, 2],
  ...
		

Links

• Alois P. Heinz, Rows n = 1..100, flattened
• J. Levine and R. E. Dalton, Minimum Periods, Modulo p, of First Order Bell Exponential Integrals, Mathematics of Computation, 16 (1962), 416-423. See Table 2.

Crossrefs

Cf. A000110, A054767.

Programs

Maple

T:= n-> (p-> seq(combinat[bell](k) mod p, k=0..p))(ithprime(n)):
seq(T(n), n=1..10);  # Alois P. Heinz, Jun 07 2023

Mathematica

A214810row[n_]:=Mod[BellB[Range[0,Prime[n]]],Prime[n]];Array[A214810row,50] (* Paolo Xausa, Aug 07 2023 *)