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A141027 a(n) = smallest number m which without its leftmost digit is equal to m/n (or 0 if no such number exists). 0

%I #6 Aug 09 2015 23:25:58

%S 0,15,0,25,12,35,0,45,0,11,0,65,0,75,32,85,0,95,0,21,0,0,0,625,52,0,0,

%T 725,0,31,0,825,0,0,72,925,0,0,0,41,0,0,0,0,92,0,0,6125,0,51,0,0,0,0,

%U 0,7125,0,0,0,61,0,0,0,8125,0,0,0,0,0,71,0,9125,0,0,304,0,0,0,0,81,0,0,0

%N a(n) = smallest number m which without its leftmost digit is equal to m/n (or 0 if no such number exists).

%F For n>10, a(n) is nonzero only if n-1 divides k*10^s for some positive integers k<=9 and s. For minimum such number k*10^s, we have a(n) = n*k*10^s/(n-1). - _Max Alekseyev_, Apr 13 2009

%e a(7) = 35: 35/7 = 5 = 35 with leftmost digit deleted.

%o (PARI) { a(n) = if(n<=10,return([0,0,15,0,25,12,35,0,45,0][n])); t=[valuation(n-1,2),valuation(n-1,5)]; k=(n-1)\2^t[1]\5^t[2]; if(k>9,return(0)); while(t[1]>t[2]&&2*k<=9,k*=2;t[1]--); while(t[1]<t[2]&&5*k<=9,k*=5;t[2]--); (k*10^vecmax(t)*n)\(n-1) } \\ _Max Alekseyev_, Apr 13 2009

%K nonn,base

%O 2,2

%A _Lekraj Beedassy_, Jul 29 2008

%E Corrected and extended by _Max Alekseyev_, Apr 13 2009

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Last modified September 14 15:51 EDT 2024. Contains 375924 sequences. (Running on oeis4.)