OFFSET
3,1
COMMENTS
The persistence of a number is the number of times you need to multiply the digits together before reaching a single digit.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 3..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) = 4*n-floor(n/6) for n > 5.
EXAMPLE
a(3) = 26 because 26 = [222]->[22]->[11]->[1] and no fewer n has persistence 3 in base 3.
MATHEMATICA
With[{m = 3}, Table[Block[{k = 1}, While[Length@ FixedPointList[Times @@ IntegerDigits[#, n] &, k, 100] != m + 2, k++]; k], {n, 3, 5}]]~Join~Array[4 # - Floor[#/6] &, 45, 6] (* Michael De Vlieger, Aug 30 2021 *)
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Sascha Kurz, Oct 08 2001
STATUS
approved