This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A166226 #31 Nov 11 2024 20:30:32
%S A166226 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,
%T A166226 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,
%U A166226 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
%N A166226 Bell number n modulo n.
%C A166226 a(n) = 2 (mod n) when n is prime.
%H A166226 G. C. Greubel, <a href="/A166226/b166226.txt">Table of n, a(n) for n = 1..10000</a>
%H A166226 Greg Hurst, Andrew Schultz, <a href="http://arxiv.org/abs/0906.0696v2">An elementary (number theory) proof of Touchard's congruence</a>, arXiv:0906.0696 [math.CO], (2009)
%F A166226 a(n) = A000110(n) mod n.
%F A166226 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
%e A166226 a(3)=a(5)=a(7)=a(11)=2.
%p A166226 seq(combinat:-bell(n) mod n, n=1..100); # _Robert Israel_, Feb 03 2016
%t A166226 Array[n \[Function] Mod[BellB[n], n], 1000] (* J. Mulder (jasper.mulder(AT)planet.nl), Jan 28 2010 *)
%t A166226 Table[Mod[BellB[n], n], {n, 1, 100}] (* _G. C. Greubel_, Feb 02 2016 *)
%o A166226 (Magma) [Bell(n) mod n: n in [1..100]]; // _Vincenzo Librandi_, Feb 03 2016
%Y A166226 See the Bell numbers sequence A000110.
%K A166226 nonn
%O A166226 1,3
%A A166226 Thierry Banel (tbanel(AT)gmail.com), Oct 09 2009
%E A166226 More terms from _R. J. Mathar_ and J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010