A046511 Numbers with multiplicative persistence value 2.

25, 26, 27, 28, 29, 34, 35, 36, 37, 38, 43, 44, 45, 46, 48, 52, 53, 54, 56, 58, 62, 63, 64, 65, 67, 72, 73, 76, 82, 83, 84, 85, 92, 99, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138, 143, 144, 145, 146, 148, 152, 153, 154, 156, 158, 162, 163, 164, 165, 167, 172

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base

Examples

			129 -> [ 18 ] -> [ 8 ] = one digit in two steps.
		

Links

• Daniel Mondot, Table of n, a(n) for n = 1..10000 (terms 1..3000 from Vincenzo Librandi)
• Eric Weisstein's World of Mathematics, Multiplicative Persistence

Crossrefs

Cf. A003001, A014120, A046502.

Programs

Mathematica

mpQ[n_]:=Length[NestWhileList[Times@@IntegerDigits[#]&,n,#>9&]]==3; Select[Range[200], mpQ] (* Harvey P. Dale, Apr 12 2014 *)

Python

from math import prod
def pd(n): return prod(map(int, str(n)))
def ok(n): return n > 9 and (p := pd(n)) > 9 and pd(p) < 10
print([k for k in range(173) if ok(k)]) # Michael S. Branicky, Jan 16 2022