A061462 The exact power of 2 that divides the n-th Bell number (A000110). Has period 12.

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

Offset: 0

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000110.

Programs

Mathematica

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

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