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A046511
Numbers with multiplicative persistence value 2.
6
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
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Sep 15 1998
STATUS
approved