A146103 Bell numbers (A000110) read mod 13.

1, 1, 2, 5, 2, 0, 8, 6, 6, 9, 2, 9, 11, 2, 3, 7, 7, 2, 8, 1, 12, 2, 11, 11, 7, 0, 5, 10, 1, 9, 10, 9, 0, 1, 0, 9, 5, 7, 5, 2, 11, 10, 6, 6, 9, 1, 1, 9, 1, 12, 12, 7, 0, 8, 3, 12, 2, 10, 2, 10, 10, 0, 11, 6, 7, 8, 11, 2, 1, 12, 12, 12, 7, 10, 11, 4, 0, 2, 6, 0, 3, 0, 11, 11, 6, 4, 8, 2, 4, 2, 8, 6, 3, 3

Offset: 0

Author

N. J. A. Sloane, Feb 07 2009

Keywords

• nonn

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 25239592216021.

Crossrefs

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

Cf. A054767 (periods).

Programs

Magma

[Bell(n) mod 13: n in [0..100]]; // Vincenzo Librandi, Feb 01 2016

Mathematica

Mod[BellB[Range[0, 100]], 13] (* G. C. Greubel, Jan 31 2016 *)

Formula

a(n+25239592216021) = a(n). - G. C. Greubel, Jan 31 2016 [See A054767. - Jianing Song, Jun 20 2025]