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

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.

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, Nov 1995

More terms from John W. Layman, Mar 19 2002

Status

approved