A146106 Bell numbers (A000110) read mod 16.

1, 1, 2, 5, 15, 4, 11, 13, 12, 11, 7, 10, 13, 5, 10, 1, 3, 12, 15, 1, 12, 15, 11, 10, 9, 9, 2, 13, 7, 4, 3, 5, 12, 3, 15, 10, 5, 13, 10, 9, 11, 12, 7, 9, 12, 7, 3, 10, 1, 1, 2, 5, 15, 4, 11, 13, 12, 11, 7, 10, 13, 5, 10, 1, 3, 12, 15, 1, 12, 15, 11, 10, 9, 9, 2, 13, 7, 4, 3, 5, 12, 3, 15, 10, 5

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, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Crossrefs

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

Cf. A054767 (periods).

Programs

Magma

[Bell(n) mod 16: n in [0..100]]; // Vincenzo Librandi, Feb 02 2016

Mathematica

Mod[BellB[Range[0, 100]], 16] (* G. C. Greubel, Feb 01 2016 *)

Formula

a(n+48) = a(n). - G. C. Greubel, Feb 01 2016 [See A054767. - Jianing Song, Jun 20 2025]