A046517 Numbers with multiplicative persistence value 8.

2677889, 2677898, 2677988, 2678789, 2678798, 2678879, 2678897, 2678978, 2678987, 2679788, 2679878, 2679887, 2687789, 2687798, 2687879, 2687897, 2687978, 2687987, 2688779, 2688797, 2688977, 2689778, 2689787, 2689877

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base

Examples

			2677889 -> [ 338688 ][ 27648 ][ 2688 ][ 768 ][ 336 ][ 54 ][ 20 ][ 0 ] -> one digit in eight steps.
		

Links

• Daniel Mondot, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Robert Israel)
• Eric Weisstein's World of Mathematics, Multiplicative Persistence

Crossrefs

Cf. A003001, A014120, A046508.

Programs

Maple

mp:= proc(n) option remember;
    if n <= 9 then return 0 fi;
    1+procname(convert(convert(n,base,10),`*`))
end proc:
select(mp=8, [$1..4000000]); # Robert Israel, Feb 12 2019

Mathematica

okQ[n_]:=Length[NestWhileList[Times@@IntegerDigits[#]&, n,IntegerLength[ #]>1&]]==9; Select[Range[2700000],okQ]  (* Harvey P. Dale, Jan 29 2011 *)

Extensions

Offset corrected by Robert Israel, Feb 12 2019