A254130 - OEIS

%I #19 May 04 2015 10:56:03

%S 0,3,5,6,7,8,9,13,16

%N Numbers whose factorials are exclusionary: numbers n such that n and n! have no digits in common.

%C Conjecture: The sequence is finite, with 16 being the last term.

%C If A182049 is finite, then this sequence is finite. If 41 is the largest term in A182049 (as is conjectured), then 16 is the largest term of this sequence. - _M. F. Hasler_, May 04 2015

%e 13! = 6227020800. 13 and 6227020800 have no digits in common, so 13 is a term of the sequence.

%t Select[Range[0,16],DisjointQ[IntegerDigits[#],IntegerDigits[#!]]&] (* _Ivan N. Ianakiev_, May 04 2015 *)

%o (PARI) is(n)=#setintersect(Set(digits(n)), Set(digits(n!)))==0

%Y Cf. A000142, A112736, A112994, A111116.

%K nonn,base,fini

%O 1,2

%A _Felix Fröhlich_, May 03 2015