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A061462 The exact power of 2 that divides the n-th Bell number (A000110). Has period 12. 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; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

{ 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, Jun 29 2001

LINKS

Amiram Eldar, Table of n, a(n) for n = 0..10000

W. F. Lunnon et al., Arithmetic properties of Bell numbers to a composite modulus I, Acta Arith., 35 (1979), 1-16.

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

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. - Paolo P. Lava, Oct 22 2008

MATHEMATICA

PadRight[{}, 120, {1, 1, 2, 1, 1, 4, 1, 1, 4, 1, 1, 2}] (* Harvey P. Dale, Sep 24 2017 *)

PROG

(PARI) a(n)=[1, 1, 2, 1, 1, 4, 1, 1, 4, 1, 1, 2][n%12+1] \\ Charles R Greathouse IV, Jul 13 2016

CROSSREFS

Cf. A000110.

Sequence in context: A327315 A141450 A209690 * A294334 A122578 A208648

Adjacent sequences:  A061459 A061460 A061461 * A061463 A061464 A061465

KEYWORD

nonn,easy

AUTHOR

Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 10 2001

STATUS

approved

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Last modified February 24 04:30 EST 2020. Contains 332197 sequences. (Running on oeis4.)