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Maximal multiplicative persistence (or length) of any n-digit number.
5

%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