

A229004


Indices of Bell numbers divisible by 3.


2



4, 8, 9, 11, 17, 21, 22, 24, 30, 34, 35, 37, 43, 47, 48, 50, 56, 60, 61, 63, 69, 73, 74, 76, 82, 86, 87, 89, 95, 99, 100, 102, 108, 112, 113, 115, 121, 125, 126, 128, 134, 138, 139, 141, 147, 151, 152, 154, 160, 164, 165, 167, 173, 177, 178, 180, 186, 190, 191
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OFFSET

1,1


COMMENTS

a(n) appears to be congruent 4, 8, 9, 11 mod 13.  Ralf Stephan, Sep 12 2013
Wagstaff shows that N(p) = (p^p1)/(p1) is the period for all primes p < 102, for p=3 then N(3) = A054767(3) = 13, Bell numbers with indices less or equal than 13 that are divisible by 3 are those with indices: 4, 8, 9, 11, so the conjecture holds.  Enrique Pérez Herrero, Sep 12 2013


LINKS

Enrique Pérez Herrero, Table of n, a(n) for n = 1..1200
J. Levine and R. E. Dalton, Minimum Periods, Modulo p, of First Order Bell Exponential Integrals, Mathematics of Computation, 16 (1962), 416423.
Samuel S. Wagstaff Jr., Aurifeuillian factorizations and the period of the Bell numbers modulo a prime, Math. Comp. 65 (1996), 383391.
Eric Weisstein's World of Mathematics, Bell Number


FORMULA

Conjecture: a(n) = a(n1)+a(n4)a(n5). G.f.: x*(2*x^4+2*x^3+x^2+4*x+4) / ((x1)^2*(x+1)*(x^2+1)).  Colin Barker, Jul 16 2014


MATHEMATICA

Select[Range[1000], Mod[BellB[#], 3] == 0&]


CROSSREFS

Cf. A000110, A016789, A155730, A054767.
Sequence in context: A228653 A158758 A317253 * A306976 A266142 A297252
Adjacent sequences: A229001 A229002 A229003 * A229005 A229006 A229007


KEYWORD

nonn


AUTHOR

Enrique Pérez Herrero, Sep 10 2013


STATUS

approved



