Jean-Claude Arbaut - cp's OEIS frontend

User: Jean-Claude Arbaut

Jean-Claude Arbaut has authored 1 sequences.

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

Jean-Claude Arbaut, Jul 08 2010

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

			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.

Cf. A000110, A003418.

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 *)

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

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

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User: Jean-Claude Arbaut

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

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