A146099 Bell numbers (A000110) read mod 9.

1, 1, 2, 5, 6, 7, 5, 4, 0, 6, 1, 6, 4, 1, 7, 5, 5, 0, 4, 5, 1, 6, 6, 1, 6, 4, 1, 1, 5, 2, 6, 4, 5, 4, 6, 3, 1, 6, 1, 1, 1, 2, 5, 6, 7, 5, 4, 0, 6, 1, 6, 4, 1, 7, 5, 5, 0, 4, 5, 1, 6, 6, 1, 6, 4, 1, 1, 5, 2, 6, 4, 5, 4, 6, 3, 1, 6, 1, 1, 1, 2, 5, 6, 7, 5, 4, 0, 6, 1, 6, 4, 1, 7, 5, 5, 0, 4, 5, 1, 6, 6, 1, 6, 4, 1

Offset

0,3

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 periodic sequences, period 39.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Formula

a(n+39) = a(n). - G. C. Greubel, Jan 31 2016 [See A054767. - Jianing Song, Jun 20 2025]

Mathematica

Mod[BellB[Range[0, 100]], 9] (* G. C. Greubel, Jan 31 2016 *)

Prog

(Magma) [Bell(n) mod 9: n in [0..100]]; // Vincenzo Librandi, Feb 01 2016
(PARI) a(n)=36825693528263826995685355884636809\8^(n%39)%8 \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

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

Cf. A054767 (periods).

Sequence in context: A273237 A278084 A225366 * A004097 A262368 A198547

Adjacent sequences: A146096 A146097 A146098 * A146100 A146101 A146102

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 07 2009

Status

approved