OFFSET
0,2
LINKS
Edson de Faria and Charles Tresser, On Sloane's persistence problem, arXiv preprint arXiv:1307.1188 [math.DS], 2013.
Edson de Faria and Charles Tresser, On Sloane's persistence problem, Experimental Math., 23 (No. 4, 2014), 363-382.
Brady Haran and Matt Parker, What's special about 277777788888899?, Numberphile video, 2019.
Tim Lamont-Smith, Multiplicative Persistence and Absolute Multiplicative Persistence, J. Int. Seq., Vol. 24 (2021), Article 21.6.7.
Stephanie Perez and Robert Styer, Persistence: A Digit Problem, Involve, Vol. 8 (2015), No. 3, 439-446.
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
2 when represented in base 2 goes 10 -> 0 and has an absolute persistence of 1, so a(1) = 2.
8 when represented in base 3 goes 22 -> 11 -> 1 and has an absolute persistence of 2, so a(2) = 8.
23 when represented in base 6 goes 35 -> 23 -> 10 -> 1 and has absolute persistence of 3, so a(3) = 23 (Cf. A064867).
52 when represented in base 9 goes 57 -> 38 -> 26 -> 13 -> 3 and has absolute persistence of 4, so a(4) = 52 (Cf. A064868).
PROG
(Python)
from math import prod
from sympy.ntheory.digits import digits
def mp(n, b): # multiplicative persistence of n in base b
c = 0
while n >= b:
n, c = prod(digits(n, b)[1:]), c+1
return c
def a(n):
k = 0
while True:
if any(mp(k, b)==n for b in range(2, max(3, k))): return k
k += 1
print([a(n) for n in range(11)]) # Michael S. Branicky, Sep 17 2021
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Tim Lamont-Smith, Nov 29 2019
EXTENSIONS
a(19)-a(27) from Giovanni Resta, Jan 20 2020
a(28)-a(30) from Michael S. Branicky, Sep 17 2021
STATUS
approved