cp's OEIS Frontend

A139285 Smallest nontrivial number m that when expressed in base n and then interpreted in base 10, is a multiple of the original number.

%I A139285 #45 Nov 09 2024 19:31:56
%S A139285 3,2,7,6,5,308,51,34217,7794416
%N A139285 Smallest nontrivial number m that when expressed in base n and then interpreted in base 10, is a multiple of the original number.
%C A139285 Not defined for n>9.
%C A139285 Note that for n=1, the unitary numeral system is used, whereas for n>=2, it is the usual base-dependent positional numeral system. - _Michel Marcus_, Sep 16 2020
%e A139285 a(1)=3 since 3 in base 1 ('unary') is 111 and, interpreted in base 10, 111 is a number divisible by 3, whereas 2 in base 1 is 11 and, interpreted in base 10, 11 is not divisible by 2.
%e A139285 a(3)=7 since 7 in base 3 is 21 and, interpreted in base 10, 21 is divisible by 7, whereas 3, 4, 5, 6 in base 3 are, respectively, 10, 11, 12, 20 and, interpreted in base 10, these are numbers not divisible, respectively, by 3, 4, 5, 6.
%e A139285 Trivial solutions (i.e., m<n for n>1 and m=n for n=1) are not considered here.
%o A139285 (Python)
%o A139285 m,M=2,11
%o A139285 while M%m>0:
%o A139285     m,M=m+1,10*M+1
%o A139285 print(1,m)
%o A139285 for n in range(2,10):
%o A139285     m,M,d=n,10,10-n
%o A139285     while M%m>0:
%o A139285         m=m+1
%o A139285         u,s=m,0
%o A139285         while u%n==0:
%o A139285             u,s=u//n,10*s+d
%o A139285         M=M+1+s
%o A139285     print(n,m)
%o A139285 # _Dimiter Skordev_, Sep 28 2020
%Y A139285 Cf. A032551, A032551, A032532.
%K A139285 base,fini,full,nonn
%O A139285 1,1
%A A139285 _Sergio Pimentel_, Jun 06 2008
%E A139285 a(9) corrected by _Giovanni Resta_, Nov 02 2017