OFFSET
1,1
COMMENTS
Numbers 0 to 9 have a multiplication persistence of 0, not 1. - Daniel Mondot, Mar 12 2022
LINKS
Daniel Mondot, Table of n, a(n) for n = 1..10000
N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.
Eric Weisstein's World of Mathematics, Multiplicative Persistence
EXAMPLE
24 -> 2 * 4 = [ 8 ] -> one digit in one step.
MATHEMATICA
Select[Range[10, 121], IntegerLength[Times @@ IntegerDigits[#]] <= 1 &] (* Jayanta Basu, Jun 26 2013 *)
PROG
(PARI) isok(n) = my(d=digits(n)); (#d > 1) && (#digits(prod(k=1, #d, d[k])) <= 1); \\ Michel Marcus, Apr 12 2018 and Mar 13 2022
(Python)
from math import prod
def ok(n): return n > 9 and prod(map(int, str(n))) < 10
print([k for k in range(134) if ok(k)]) # Michael S. Branicky, Mar 13 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Sep 15 1998
EXTENSIONS
Incorrect terms 0 to 9 removed by Daniel Mondot, Mar 12 2022
STATUS
approved