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A239427
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Numbers such that additive and multiplicative persistences coincide.
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6
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 28, 29, 30, 31, 32, 33, 37, 38, 40, 41, 42, 46, 48, 50, 51, 56, 58, 60, 61, 64, 65, 67, 70, 71, 73, 76, 80, 81, 82, 83, 84, 85, 90, 92, 99, 100, 101, 102, 103, 104, 105, 106
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OFFSET
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1,3
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COMMENTS
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LINKS
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EXAMPLE
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28 -> 10 -> 1 has additive persistence 2. 28 -> 16 -> 6 has multiplicative persistence 2. 28 is therefore in the sequence.
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PROG
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(PARI) for(n=0, 106, v=n; a=0; while(n>9, a++; n=sumdigits(n)); n=v; m=0; while(n>9, m++; d=digits(n); n=prod(k=1, #d, d[k])); n=v; if(a==m, print1(n, ", ")));
(Python)
from math import prod
ap = 0
while n > 9: n, ap = sum(map(int, str(n))), ap+1
return ap
mp = 0
while n > 9: n, mp = prod(map(int, str(n))), mp+1
return mp
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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