A179279 Composite numbers k such that (Bell(k+1) - Bell(k)) mod k = 1.

4, 28, 40, 343, 10744, 18506, 18658, 22360, 34486, 289912, 293710, 565213, 722765, 2469287, 13231942, 86523219

Offset

1,1

Comments

The congruence is true for all primes k. Bell(k) is the sequence A000110. Tested up to k=5000.

a(10) > 73000. - Giovanni Resta, Aug 26 2018

a(17) > 10^8. - Hiroaki Yamanouchi, Sep 01 2018

One could compute the Bell numbers mod lcm(1, 2, ..., k) (see A003418) (or even the lcm of the composite numbers up to k) to reduce the number of digits and still find the same terms. - David A. Corneth, Aug 26 2018

Links

Table of n, a(n) for n=1..16.

Example

For k=4, (Bell(5) - Bell(4)) mod 4 = (52 - 15) mod 4 = 37 mod 4 = 1, but 4 is not prime, so 4 is a term.

Mathematica

fQ[n_] := ! PrimeQ@n && Mod[BellB[n + 1] - BellB[n], n] == 1; k = 1; lst = {}; While[k < 9201, If[fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst (* Robert G. Wilson v, Jul 28 2010 *)

Crossrefs

Cf. A000110, A003418.

Sequence in context: A032405 A344467 A307046 * A061428 A069518 A151912

Adjacent sequences: A179276 A179277 A179278 * A179280 A179281 A179282

Keyword

nonn,more

Author

Jean-Claude Arbaut, Jul 08 2010

Extensions

a(5)-a(9) from Giovanni Resta, Aug 26 2018

a(10)-a(16) from Hiroaki Yamanouchi, Sep 01 2018

Status

approved