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

1,1

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A003001, A014120, A046502.

Sequence in context: A165846 A135218 A133507 * A140058 A199992 A242221

Adjacent sequences: A046508 A046509 A046510 * A046512 A046513 A046514

Keyword

nonn,base

Author

Patrick De Geest, Sep 15 1998

Status

approved