A014553 - OEIS

A014553

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

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

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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 nondecreasing 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.