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.

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

Offset: 1

Author

Amarnath Murthy, Sep 01 2003

Keywords

• base
• look
• nonn

Comments

Conjecture: no term is zero.

Examples

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A051801.

Programs

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

Python

from functools import reduce
from operator import mul
def A087304(n):
    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
    return i*n # Chai Wah Wu, Aug 11 2017

Formula

a(10*n) = a(n)*10. - Chai Wah Wu, Aug 11 2017

Extensions

More terms from David Wasserman, Apr 19 2005