%I #24 Dec 12 2015 07:58:51
%S 1,4,5,6,7,7,8,9,9,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,
%T 11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,
%U 11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11
%N Maximal multiplicative persistence (or length) of any n-digit number.
%C The "persistence" or "length" of an N-digit decimal number is the number of times one must iteratively form the product of its digits until one obtains a one-digit product (For another definition see A003001.)
%C For all other n<2530, a(n)=11 because sequence is nondecreasing and a number with multiplicative persistence 12 must have more than 2530 digits. - _Sascha Kurz_, Mar 24 2002
%D Gottlieb, A. J. Problems 28-29 in "Bridge, Group Theory and a Jigsaw Puzzle." Techn. Rev. 72, unpaginated, Dec. 1969.
%D Gottlieb, A. J. Problem 29 in "Integral Solutions, Ladders and Pentagons." Techn. Rev. 72, unpaginated, Apr. 1970.
%H Beeler, M., Gosper, R. W. and Schroeppel, R., <a href="http://www.inwap.com/pdp10/hbaker/hakmem/number.html#item56">HAKMEM, ITEM 56</a>
%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/persistence.html">The persistence of a number</a>, J. Recreational Math., 6 (1973), 97-98.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativePersistence.html">Multiplicative Persistence.</a>
%e 168889 is not in A003001 because a(6) = a(5) = 7.
%Y Cf. A003001, A031346, A035927.
%K nonn,easy,base
%O 1,2
%A _Eric W. Weisstein_
%E Corrected by _N. J. A. Sloane_, Nov 1995
%E More terms from _John W. Layman_, Mar 19 2002