# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a139285 Showing 1-1 of 1 %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., m1 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,changed %O A139285 1,1 %A A139285 _Sergio Pimentel_, Jun 06 2008 %E A139285 a(9) corrected by _Giovanni Resta_, Nov 02 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE