A046513 Numbers with multiplicative persistence value 4.

77, 177, 268, 277, 286, 348, 355, 377, 378, 379, 384, 387, 397, 438, 446, 464, 467, 476, 477, 483, 489, 498, 535, 553, 557, 575, 628, 644, 647, 668, 674, 677, 678, 682, 686, 687, 699, 717, 727, 737, 738, 739, 746, 747, 755, 764, 767, 768, 771, 772, 773

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

Cf. A003001, A014120, A046504.

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=4, [$1..1000]); # Robert Israel, Feb 12 2019

Mathematica

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

Extensions

Offset corrected by Robert Israel, Feb 12 2019