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A239427

Numbers such that additive and multiplicative persistences coincide.

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

1,3

COMMENTS

Numbers n for which A031286(n) = A031346(n).

LINKS

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..66 from Arkadiusz Wesolowski)

Eric Weisstein's World of Mathematics, Additive Persistence

Eric Weisstein's World of Mathematics, Multiplicative Persistence

EXAMPLE

28 -> 10 -> 1 has additive persistence 2. 28 -> 16 -> 6 has multiplicative persistence 2. 28 is therefore in the sequence.

PROG

(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

def A031286(n):

ap = 0

while n > 9: n, ap = sum(map(int, str(n))), ap+1

return ap

def A031346(n):

mp = 0

while n > 9: n, mp = prod(map(int, str(n))), mp+1

return mp

def ok(n): return A031286(n) == A031346(n)

print([k for k in range(107) if ok(k)]) # Michael S. Branicky, Sep 17 2022