A046507 -id:A046507 - cp's OEIS frontend

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

Patrick De Geest, Sep 15 1998

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)

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

Robert Israel, Table of n, a(n) for n = 1..10000
Daniel Mondot, Multiplicative Persistence Tree
Eric Weisstein's World of Mathematics, Multiplicative Persistence

Cf. A003001, A014120, A046507, A350185.

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

A199997 Composite numbers whose multiplicative persistence is 7.

Original entry on oeis.org

68889, 68898, 68988, 69888, 86889, 86898, 86988, 88689, 88698, 88869, 88896, 88968, 88986, 89688, 89868, 89886, 96888, 98688, 98868, 98886, 168889, 168898, 168988, 169888, 186898, 186988, 188689, 188698, 188896, 188968, 188986, 189688, 189868, 189886, 196888

Offset: 1

Jaroslav Krizek, Nov 13 2011

Complement of A046507 with respect to A046516.

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

Cf. A046507 (primes whose multiplicative persistence is 7).

persistence[n_] := Module[{cnt = 0, k = n}, While[k > 9, cnt++; k = Times @@ IntegerDigits[k]]; cnt]; Select[Range[300000], ! PrimeQ[#] && persistence[#] == 7 &] (* T. D. Noe, Nov 23 2011 *)

cp's OEIS Frontend

A046516 Numbers with multiplicative persistence value 7.

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