OFFSET
0,1
COMMENTS
The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit.
LINKS
C. Rivera, Puzzle page
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
47 -> 28 -> 16 -> 6 has persistence 3.
MATHEMATICA
a[n_]:=Length[NestWhileList[Times@@IntegerDigits[#]&, n, #>9&]]-1; t={}; i=1; Do[While[a[p=Prime[i]]!=n, i++]; AppendTo[t, p], {n, 0, 9}]; t (* Jayanta Basu, Jun 02 2013 *)
CROSSREFS
KEYWORD
nonn,base,more,hard,nice,changed
AUTHOR
Patrick De Geest, Sep 15 1998
EXTENSIONS
Value for n=10 and n=11 found by Jud McCranie
STATUS
approved