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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 (list; graph; refs; listen; history; text; internal format)
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^p-1)/(p-1) 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), 416-423.

Samuel S. Wagstaff Jr., Aurifeuillian factorizations and the period of the Bell numbers modulo a prime, Math. Comp. 65 (1996), 383-391.

Eric Weisstein's World of Mathematics, Bell Number

FORMULA

Conjecture: a(n) = a(n-1)+a(n-4)-a(n-5). G.f.: x*(2*x^4+2*x^3+x^2+4*x+4) / ((x-1)^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

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Last modified October 1 17:45 EDT 2020. Contains 337444 sequences. (Running on oeis4.)