

A087304


Smallest nontrivial multiple of n whose nonzero digit product is the same as that of the nonzero digit product of n. By nontrivial one means a(n) is not equal to n or (10^k)*n. 0 if no such number exists.


2



11, 12, 1113, 104, 15, 132, 1071, 24, 11133, 110, 1001, 1020, 1131, 1022, 105, 32, 1071, 108, 133, 120, 100002, 1122, 161, 1008, 125, 1430, 702, 224, 3016, 11130, 10013, 160, 3003, 612, 315, 1332, 703, 342, 11193, 1040, 10004, 1008, 602, 1144, 225
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OFFSET

1,1


COMMENTS

Conjecture: no term is zero.


LINKS



FORMULA



EXAMPLE

a(19) = 133 = 19*7 and 1*3*3 = 1*9.


PROG

(Python)
from functools import reduce
from operator import mul
i, p = 2, reduce(mul, (int(d) for d in str(n) if d != '0'))
while (max(str(i)) == '1' and str(i).count('1') == 1) or reduce(mul, (int(d) for d in str(i*n) if d != '0')) != p:
i += 1
(PARI) prd(n) = {my(d = digits(n), p = 1); for (k=1, #d, if (d[k], p *= d[k]); ); p; }
a(n) = {my(k = 2, prdn = prd(n)); while (prd(k*n) != prdn, k++; if (! (k % 10), k++)); k*n; } \\ Michel Marcus, Aug 12 2017


CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



