A046516 Numbers with multiplicative persistence value 7.

68889, 68898, 68988, 69888, 86889, 86898, 86988, 88689, 88698, 88869, 88896, 88968, 88986, 89688, 89868, 89886, 96888, 98688, 98868, 98886, 168889, 168898, 168988, 169888, 186889, 186898, 186988, 188689, 188698, 188869, 188896, 188968

Offset

1,1

Comments

From Daniel Mondot, Mar 26 2022: (Start)

The product of the digits of each term is 27648, 47628, 64827, 84672, 134217728, 914838624, 1792336896, 3699376128, 48814981614, 134481277728, 147483721728 or 1438916737499136 (sequence A350185).

The first 62 terms produce 27648.

The first term that produces 47628 is a(63).

The first term that produces 64827 is a(233).

The first term that produces 84672 is a(235).

The first term that produces 134217728 is a(1753110).

The first term that produces 914838624 is a(17835449).

The first term that produces 1792336896 is a(18235677).

The first term that produces 3699376128 is a(23853261).

The first term that produces 48814981614 is a(66441891).

The first term that produces 134481277728 is a(452601087).

The first term that produces 147483721728 is a(425636434).

The first term that produces 1438916737499136 is somewhere after a(500*10^6). (End)

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Daniel Mondot, Multiplicative Persistence Tree

Eric Weisstein's World of Mathematics, Multiplicative Persistence

Example

68889 -> [ 27648 ][ 2688 ][ 768 ][ 336 ][ 54 ][ 20 ][ 0 ] -> one digit in seven steps.

Maple

mp:= proc(n) option remember;
    if n <= 9 then return 0 fi;
    1+procname(convert(convert(n, base, 10), `*`))
end proc:
select(mp=7, [$1..200000]); # Robert Israel, Feb 12 2019

Crossrefs

Cf. A003001, A014120, A046507, A350185.

Sequence in context: A213702 A233721 A121107 * A199997 A250500 A354194

Adjacent sequences: A046513 A046514 A046515 * A046517 A046518 A046519

Keyword

nonn,base

Author

Patrick De Geest, Sep 15 1998

Status

approved