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 A179279 Composite numbers n such that (Bell(n+1) - Bell(n)) mod n = 1. 0
 4, 28, 40, 343, 10744, 18506, 18658, 22360, 34486, 289912, 293710, 565213, 722765, 2469287, 13231942, 86523219 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The congruence is true for all primes n. Bell(n) is the sequence A000110. Tested up to n=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, ..., n) (see A003418), (or even the lcm of the composite number up to n) to reduce the number of digits and still find the same terms. - David A. Corneth, Aug 26 2018 LINKS EXAMPLE For n=4, (Bell(5) - Bell(4)) mod 4 = (52 - 15) mod 4 = 37 mod 4 = 1, but 4 is not prime. 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: A043074 A137314 A032405 * 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

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Last modified October 23 06:29 EDT 2018. Contains 316520 sequences. (Running on oeis4.)