1,2

For p prime, a(p) divides (p^p-1)/(p-1) = A023037(p), with equality at least for p up to 19.

Wagstaff shows that N(p) = (p^p-1)/(p-1) is the period for all primes p < 102 and for primes p = 113, 163, 167 and 173. For p = 7547, N(p) is a probable prime, which means that this p may have the maximum possible period N(p) also. See A088790. [From T. D. Noe (noe(AT)sspectra.com), Dec 17 2008]

J. Levine and R. E. Dalton, Minimum Periods, Modulo p, of First Order Bell Exponential Integrals, Mathematics of Computation, 16 (1962), 416-423.

W. F. Lunnon et al., Arithmetic properties of Bell numbers to a composite modulus I, Acta Arith., 35 (1979), 1-16. [From N. J. A. Sloane (njas(AT)research.att.com), Feb 07 2009]

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Samuel S. Wagstaff Jr., Aurifeuillian factorizations and the period of the Bell numbers modulo a prime, Math. Comp. 65 (1996), 383-391. [From T. D. Noe (noe(AT)sspectra.com), Dec 17 2008]

If gcd(n,m) = 1, a(n*m) = lcm(a(n), a(m)). But the sequence is not in general multiplicative; e.g. a(2) = 3, a(9) = 39 and a(18) = 39. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 06 2006

Cf. A000110, A023037.

Sequence in context: A142351 A121565 A107733 this_sequence A137947 A076747 A043055

Adjacent sequences: A054764 A054765 A054766 this_sequence A054768 A054769 A054770

nonn,hard,nice

Eric Weisstein (eric(AT)weisstein.com), Feb 09, 2002

More information from Phil Carmody (pc+oeis(AT)asdf.org), Dec 22 2002

Extended by T. D. Noe (noe(AT)sspectra.com), Dec 18 2008