cp's OEIS Frontend

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.

%I A087304 #12 Aug 12 2017 02:25:33
%S A087304 11,12,1113,104,15,132,1071,24,11133,110,1001,1020,1131,1022,105,32,
%T A087304 1071,108,133,120,100002,1122,161,1008,125,1430,702,224,3016,11130,
%U A087304 10013,160,3003,612,315,1332,703,342,11193,1040,10004,1008,602,1144,225
%N 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.
%C A087304 Conjecture: no term is zero.
%H A087304 Chai Wah Wu, <a href="/A087304/b087304.txt">Table of n, a(n) for n = 1..10000</a>
%F A087304 a(10*n) = a(n)*10. - _Chai Wah Wu_, Aug 11 2017
%e A087304 a(19) = 133 = 19*7 and 1*3*3 = 1*9.
%o A087304 (Python)
%o A087304 from functools import reduce
%o A087304 from operator import mul
%o A087304 def A087304(n):
%o A087304     i, p = 2, reduce(mul,(int(d) for d in str(n) if d != '0'))
%o A087304     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:
%o A087304         i += 1
%o A087304     return i*n # _Chai Wah Wu_, Aug 11 2017
%o A087304 (PARI) prd(n) = {my(d = digits(n), p = 1); for (k=1, #d, if (d[k], p *= d[k]);); p;}
%o A087304 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
%Y A087304 Cf. A051801.
%K A087304 base,look,nonn
%O A087304 1,1
%A A087304 _Amarnath Murthy_, Sep 01 2003
%E A087304 More terms from _David Wasserman_, Apr 19 2005