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The exact power of 2 that divides the n-th Bell number (A000110). Has period 12.

+0
2

1, 1, 2, 1, 1, 4, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 4, 1, 1, 2 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`{ Bell(n) mod 8 } is periodic with period 24, the period being (1 1 2 5 7 4 3 5 4 3 7 2 5 5 2 1 3 4 7 1 4 7 3 2). Hence the highest power of 2 dividing a Bell number is 4. - David W. Wilson (davidwwilson(AT)comcast.net), Jun 29, 2001`
	REFERENCES	`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) 1-16.`
	FORMULA	`a(n)=(1/396){43(n mod 12)-23[(n+1) mod 12]+10[(n+2) mod 12]+109[(n+3) mod 12]-89[(n+4) mod 12]+10[(n+5) mod 12]+109[(n+6) mod 12]-89[(n+7) mod 12]+10[(n+8) mod 12]+43[(n+9) mod 12]-23[(n+10) mod 12]+10*[(n+11) mod 12]}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Oct 22 2008]`
	CROSSREFS	`Cf. A000110.` `Sequence in context: A008307 A099238 A141450 this_sequence A122578 A005131 A105477` `Adjacent sequences: A061459 A061460 A061461 this_sequence A061463 A061464 A061465`
	KEYWORD	`nonn`
	AUTHOR	`Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 10 2001`

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Last modified November 30 13:13 EST 2009. Contains 167758 sequences.

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