A166226 Bell number n modulo n.

0, 0, 2, 3, 2, 5, 2, 4, 6, 5, 2, 1, 2, 12, 5, 3, 2, 13, 2, 12, 15, 5, 2, 9, 3, 18, 10, 3, 2, 27, 2, 12, 4, 5, 0, 1, 2, 24, 28, 27, 2, 23, 2, 8, 5, 5, 2, 33, 24, 20, 49, 39, 2, 5, 27, 28, 34, 5, 2, 57, 2, 36, 6, 51, 47, 19, 2, 52, 15, 25, 2, 49, 2, 42, 22, 71, 59, 19, 2, 44, 23, 5, 2, 65, 84

Offset

1,3

Comments

a(n) = 2 (mod n) when n is prime.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Greg Hurst, Andrew Schultz, An elementary (number theory) proof of Touchard's congruence, arXiv:0906.0696 [math.CO], (2009)

Formula

a(n) = A000110(n) mod n.

a(p^m) = m+1 (mod p) when p is prime and m >= 1 (see Lemma 3.1 in the Hurst/Schultz reference). - Joerg Arndt, Jun 01 2016

Example

a(3)=a(5)=a(7)=a(11)=2.

Maple

seq(combinat:-bell(n) mod n, n=1..100); # Robert Israel, Feb 03 2016

Mathematica

Array[n \[Function] Mod[BellB[n], n], 1000] (* J. Mulder (jasper.mulder(AT)planet.nl), Jan 28 2010 *)
Table[Mod[BellB[n], n], {n, 1, 100}] (* G. C. Greubel, Feb 02 2016 *)

Prog

(Magma) [Bell(n) mod n: n in [1..100]]; Vincenzo Librandi, Feb 03 2016

Crossrefs

See the Bell numbers sequence A000110.

Sequence in context: A319431 A258581 A108501 * A263978 A326810 A263726

Adjacent sequences: A166223 A166224 A166225 * A166227 A166228 A166229

Keyword

nonn

Author

Thierry Banel (tbanel(AT)gmail.com), Oct 09 2009

Extensions

More terms from R. J. Mathar and J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010

Status

approved