A146109 Bell numbers (A000110) read mod 19.

1, 1, 2, 5, 15, 14, 13, 3, 17, 0, 18, 4, 5, 7, 14, 16, 15, 1, 10, 2, 3, 7, 1, 10, 8, 16, 1, 17, 18, 3, 9, 12, 2, 11, 12, 16, 11, 12, 5, 10, 8, 11, 18, 5, 17, 18, 16, 2, 12, 2, 14, 13, 4, 9, 8, 4, 17, 15, 18, 0, 10, 4, 3, 16, 15, 18, 14, 14, 16, 8, 17, 13, 17, 12, 2, 13, 14, 18, 10, 14, 7, 0, 12

Offset: 0

Author

N. J. A. Sloane, Feb 07 2009

Keywords

• nonn

Comments

Conjecture: a(n+109912203092239643840221) = a(n). - G. C. Greubel, Feb 01 2016 [Conjecture is correct; see A054767. - Jianing Song, Jun 20 2025]

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• W. F. Lunnon, P. A. B. Pleasants, and N. M. Stephens, Arithmetic properties of Bell numbers to a composite modulus I, Acta Arithmetica 35 (1979), pp. 1-16.
• Index entries for linear recurrences with constant coefficients, order 109912203092239643840221.

Crossrefs

Cf. A000110, A146093-A146122 (Bell numbers read mod 3 to mod 32).

Cf. A054767 (periods).

Programs

Magma

[Bell(n) mod 19: n in [0..100]]; // Vincenzo Librandi, Feb 02 2016

Mathematica

Mod[BellB[Range[0,90]],19] (* Harvey P. Dale, May 04 2014 *)