A146119 Bell numbers (A000110) read mod 29.

1, 1, 2, 5, 15, 23, 0, 7, 22, 6, 4, 28, 13, 13, 7, 20, 28, 17, 16, 20, 20, 15, 5, 25, 7, 24, 11, 21, 18, 2, 3, 7, 20, 9, 23, 7, 0, 28, 10, 3, 12, 26, 20, 27, 19, 16, 4, 7, 11, 6, 20, 1, 3, 2, 6, 3, 10, 20, 5, 10, 27, 0, 3, 1, 7, 28, 9, 13, 15, 9, 17, 18, 17, 6, 20, 11, 18, 17, 26, 21, 4, 5

Offset: 0

Author

N. J. A. Sloane, Feb 07 2009

Keywords

• nonn

Comments

Conjecture: a(n+91703076898614683377208150526107718802981) = a(n). - G. C. Greubel, Feb 02 2016

This is correct, see A054767; the period is (29^29-1)/(29-1). - Joerg Arndt, Jun 19 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 91703076898614683377208150526107718802981.

Crossrefs

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

Cf. A054767 (periods).

Programs

Magma

[Bell(n) mod 29: n in [0..100]]; // G. C. Greubel, Feb 02 2016

Mathematica

Mod[BellB[Range[0, 100]], 29] (* G. C. Greubel, Feb 02 2016 *)