A146094 Bell numbers (A000110) read mod 4.

1, 1, 2, 1, 3, 0, 3, 1, 0, 3, 3, 2, 1, 1, 2, 1, 3, 0, 3, 1, 0, 3, 3, 2, 1, 1, 2, 1, 3, 0, 3, 1, 0, 3, 3, 2, 1, 1, 2, 1, 3, 0, 3, 1, 0, 3, 3, 2, 1, 1, 2, 1, 3, 0, 3, 1, 0, 3, 3, 2, 1, 1, 2, 1, 3, 0, 3, 1, 0, 3, 3, 2, 1, 1, 2, 1, 3, 0, 3, 1, 0, 3, 3, 2, 1, 1, 2, 1, 3, 0, 3, 1, 0, 3, 3, 2, 1, 1, 2, 1, 3, 0, 3, 1, 0

Offset: 0

Author

N. J. A. Sloane, Feb 07 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2500
• P. Pleasants, W. Lunnon, and N. 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 (0,0,0,0,0,0,0,0,0,0,0,1).

Crossrefs

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

Cf. A054767 (periods).

Programs

Magma

[Bell(n) mod 4: n in [0..100]]; // Vincenzo Librandi, Jan 30 2016

Mathematica

Mod[BellB[Range[0, 50]], 4] (* G. C. Greubel, Jan 30 2016 *)

Formula

a(n) = a(n-12). - Charles R Greathouse IV, Jul 06 2011 [See A054767. - Jianing Song, Jun 20 2025]