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A046516 Numbers with multiplicative persistence value 7.

%I A046516 #31 Feb 16 2025 08:32:39
%S A046516 68889,68898,68988,69888,86889,86898,86988,88689,88698,88869,88896,
%T A046516 88968,88986,89688,89868,89886,96888,98688,98868,98886,168889,168898,
%U A046516 168988,169888,186889,186898,186988,188689,188698,188869,188896,188968
%N A046516 Numbers with multiplicative persistence value 7.
%C A046516 From _Daniel Mondot_, Mar 26 2022: (Start)
%C A046516 The product of the digits of each term is 27648, 47628, 64827, 84672, 134217728, 914838624, 1792336896, 3699376128, 48814981614, 134481277728, 147483721728 or 1438916737499136 (sequence A350185).
%C A046516 The first 62 terms produce 27648.
%C A046516 The first term that produces 47628 is a(63).
%C A046516 The first term that produces 64827 is a(233).
%C A046516 The first term that produces 84672 is a(235).
%C A046516 The first term that produces 134217728 is a(1753110).
%C A046516 The first term that produces 914838624 is a(17835449).
%C A046516 The first term that produces 1792336896 is a(18235677).
%C A046516 The first term that produces 3699376128 is a(23853261).
%C A046516 The first term that produces 48814981614 is a(66441891).
%C A046516 The first term that produces 134481277728 is a(452601087).
%C A046516 The first term that produces 147483721728 is a(425636434).
%C A046516 The first term that produces 1438916737499136 is somewhere after a(500*10^6). (End)
%H A046516 Robert Israel, <a href="/A046516/b046516.txt">Table of n, a(n) for n = 1..10000</a>
%H A046516 Daniel Mondot, <a href="https://oeis.org/wiki/File:Multiplicative_Persistence_Tree.txt">Multiplicative Persistence Tree</a>
%H A046516 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiplicativePersistence.html">Multiplicative Persistence</a>
%e A046516 68889 -> [ 27648 ][ 2688 ][ 768 ][ 336 ][ 54 ][ 20 ][ 0 ] -> one digit in seven steps.
%p A046516 mp:= proc(n) option remember;
%p A046516     if n <= 9 then return 0 fi;
%p A046516     1+procname(convert(convert(n,base,10),`*`))
%p A046516 end proc:
%p A046516 select(mp=7, [$1..200000]); # _Robert Israel_, Feb 12 2019
%Y A046516 Cf. A003001, A014120, A046507, A350185.
%K A046516 nonn,base
%O A046516 1,1
%A A046516 _Patrick De Geest_, Sep 15 1998