A046513 - OEIS

%I #17 Feb 16 2025 08:32:39

%S 77,177,268,277,286,348,355,377,378,379,384,387,397,438,446,464,467,

%T 476,477,483,489,498,535,553,557,575,628,644,647,668,674,677,678,682,

%U 686,687,699,717,727,737,738,739,746,747,755,764,767,768,771,772,773

%N Numbers with multiplicative persistence value 4.

%H Robert Israel, <a href="/A046513/b046513.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiplicativePersistence.html">Multiplicative Persistence</a>

%e 737 -> [ 147 ][ 28 ][ 16 ][ 6 ] -> one digit in four steps.

%p mp:= proc(n) option remember;

%p     if n <= 9 then return 0 fi;

%p     1+procname(convert(convert(n,base,10),`*`))

%p end proc:

%p select(mp=4, [$1..1000]); # _Robert Israel_, Feb 12 2019

%t pr4Q[n_] := Length[NestWhileList[Times @@ IntegerDigits[#] &, n, # > 9 &]] == 5; Select[Range[773], pr4Q] (* _Jayanta Basu_, Jun 26 2013 *)

%Y Cf. A003001, A014120, A046504.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Sep 15 1998

%E Offset corrected by _Robert Israel_, Feb 12 2019