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A166226
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Bell number n modulo n.
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1
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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
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OFFSET
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1,3
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COMMENTS
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a(n) = 2 (mod n) when n is prime.
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LINKS
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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)
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FORMULA
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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
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EXAMPLE
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a(3)=a(5)=a(7)=a(11)=2.
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MAPLE
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seq(combinat:-bell(n) mod n, n=1..100); # Robert Israel, Feb 03 2016
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MATHEMATICA
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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 *)
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PROG
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(MAGMA) [Bell(n) mod n: n in [1..100]]; Vincenzo Librandi, Feb 03 2016
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CROSSREFS
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See the Bell numbers sequence A000110.
Sequence in context: A319431 A258581 A108501 * A263978 A326810 A263726
Adjacent sequences: A166223 A166224 A166225 * A166227 A166228 A166229
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KEYWORD
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nonn
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AUTHOR
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Thierry Banel (tbanel(AT)gmail.com), Oct 09 2009
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EXTENSIONS
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More terms from R. J. Mathar and J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010
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STATUS
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approved
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