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A330152
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Absolute multiplicative persistence: a(n) is the least number with multiplicative persistence n for some base b > 1.
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0
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0, 2, 8, 23, 52, 127, 218, 412, 542, 692, 1471, 2064, 2327, 4739, 13025, 16213, 20388, 45407, 82605, 123706, 207778, 323382, 605338, 905670, 1033731, 2041995, 3325970, 4282238, 7638962, 9840138, 10364329
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OFFSET
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0,2
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LINKS
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EXAMPLE
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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).
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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