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

1,1

Comments

Conjecture: no term is zero.

Links

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

Formula

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

Example

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

Prog

(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
(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

Cf. A051801.

Sequence in context: A042097 A056684 A042731 * A340204 A121808 A160265

Adjacent sequences: A087301 A087302 A087303 * A087305 A087306 A087307

Keyword

base,look,nonn

Author

Amarnath Murthy, Sep 01 2003

Extensions

More terms from David Wasserman, Apr 19 2005

Status

approved