OFFSET
5,1
COMMENTS
The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit. a(3) and a(4) seem not to exist.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 5..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.
Carlos Rivera, Puzzle 22. Primes and Persistence, The Prime Puzzles and Problems Connection.
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) = 6*n-floor(n/120) for n > 119.
EXAMPLE
a(9)=394 because 394=[477]->[237]->[46]->[26]->[13]->[3] and no smaller n has persistence 5 in base 9.
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Sascha Kurz, Oct 09 2001
STATUS
approved