OFFSET
7,1
COMMENTS
The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit. a(5)=1811981201171874, a(6) seems not to exist.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 7..10000
M. R. Diamond and D. D. Reidpath, A counterexample to a conjecture of Sloane and Erdos, J. Recreational Math., 1998 29(2), 89-92.
Sascha Kurz, Persistence in different bases
T. Lamont-Smith, Multiplicative Persistence and Absolute Multiplicative Persistence, J. Int. Seq., Vol. 24 (2021), Article 21.6.7.
C. Rivera, Minimal prime with persistence p
N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.
Eric Weisstein's World of Mathematics, Multiplicative Persistence
FORMULA
a(n) = 7*n-[n/720] for n > 719.
EXAMPLE
a(13) = 439 because 439 = [2'7'10]->[10'10]->[7'9]->[4'11]->[3'5]->[1'2]->[2] needs 6 steps and no fewer n.
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Sascha Kurz, Oct 08 2001
STATUS
approved