A075013 Smallest k such that the decimal concatenation of k and k+1 is divisible by n.
1, 1, 1, 1, 4, 1, 5, 5, 4, 9, 16, 1, 7, 5, 4, 19, 3, 13, 22, 19, 16, 27, 2, 19, 24, 7, 31, 5, 31, 19, 27, 19, 16, 3, 9, 31, 26, 41, 7, 19, 28, 37, 20, 27, 4, 51, 20, 19, 16, 49, 52, 35, 32, 31, 49, 5, 22, 31, 66, 19, 32, 27, 58, 19, 9, 49, 6, 35, 28, 9, 26, 67, 13, 63, 49, 79, 16
Offset: 1
Examples
a(16) = 19 as 16 divides 1920.
Programs
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Mathematica
With[{cnct=Table[FromDigits[Flatten[IntegerDigits/@{n,n+1}]],{n,100}]},Table[ Position[cnct,?(Divisible[#,k]&),1,1],{k,100}]]//Flatten (* _Harvey P. Dale, Apr 11 2020 *) -
PARI
for(n=1,100,k=1:while((k*(10^floor(log(k+1)/log(10)+1))+k+1)%n>0,k=k+1):print1(k","))
Extensions
Corrected and extended by Ralf Stephan, Mar 23 2003