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A014553 Maximal multiplicative persistence (or length) of any n-digit number. 4
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, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.)

For all other n<2530, a[n]=11 because sequence is non-decreasing and a number with multiplicative persistence 12 must have more than 2530 digits. - Sascha Kurz, Mar 24 2002

REFERENCES

Gottlieb, A. J. Problems 28-29 in ``Bridge, Group Theory and a Jigsaw Puzzle.'' Techn. Rev. 72, unpaginated, Dec. 1969.

Gottlieb, A. J. Problem 29 in ``Integral Solutions, Ladders and Pentagons.'' Techn. Rev. 72, unpaginated, Apr. 1970.

LINKS

Table of n, a(n) for n=1..72.

Beeler, M., Gosper, R. W. and Schroeppel, R., HAKMEM, ITEM 56

N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.

Eric Weisstein's World of Mathematics, Multiplicative Persistence.

EXAMPLE

168889 is not in A003001 because a(6) = a(5) = 7

CROSSREFS

Cf. A003001, A031346, A035927.

Sequence in context: A114546 A067471 A102691 * A227422 A121855 A239440

Adjacent sequences:  A014550 A014551 A014552 * A014554 A014555 A014556

KEYWORD

nonn,easy,base

AUTHOR

Eric W. Weisstein

EXTENSIONS

Corrected by N. J. A. Sloane 11/95.

More terms from John W. Layman, Mar 19 2002

STATUS

approved

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Last modified July 23 08:10 EDT 2014. Contains 244850 sequences.