A146121 Bell numbers (A000110) read mod 31.

1, 1, 2, 5, 15, 21, 17, 9, 17, 5, 4, 11, 15, 1, 20, 30, 16, 8, 1, 21, 3, 25, 26, 19, 16, 2, 15, 16, 17, 12, 3, 2, 3, 7, 20, 5, 7, 26, 26, 22, 9, 15, 26, 16, 21, 19, 15, 24, 9, 22, 24, 28, 20, 14, 4, 18, 17, 0, 2, 29, 15, 5, 5, 10, 27, 25, 12, 2, 21, 17, 0, 24, 10, 11, 6, 9, 3, 8, 2, 0, 15, 21

Offset: 0

Author

N. J. A. Sloane, Feb 07 2009

Keywords

• nonn

Comments

Conjecture: a(n+568972471024107865287021434301977158534824481) = a(n). - G. C. Greubel, Feb 02 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 568972471024107865287021434301977158534824481.

Crossrefs

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

Cf. A054767 (periods).

Programs

Magma

[Bell(n) mod 31: n in [0..100]]; // G. C. Greubel, Feb 02 2016

Mathematica

Mod[BellB[Range[0, 100]], 31] (* G. C. Greubel, Feb 02 2016 *)