A226219 - OEIS

%I #11 Apr 25 2016 12:00:15

%S 2,11,6,11,6,3,6,11,6,11,11,101,26,87,51,21,26,69,51,63,6,58,51,97,26,

%T 5,51,101,26,79,11,101,26,101,51,21,26,101,51,87,6,59,34,101,26,21,51,

%U 74,26,51,3,69,26,29,51,21,26,101,51,27,6,92,51,26,26,21

%N Least k > 1 not a power of 10 such that n is a substring of k*n.

%H Paul Tek, <a href="/A226219/b226219.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) <= 10^A055642(n)+1.

%t Table[k = 2; While[IntegerQ[Log[10, k]] || StringPosition[ToString[k*n], ToString[n], 1] == {}, k++]; k, {n, 0, 100}] (* _T. D. Noe_, May 31 2013 *)

%o (Perl) sub a {

%o     my $n = shift;

%o     my $k = 2;

%o     while (1) {

%o         if ($k !~ /^10+$/) {

%o             if (index($k*$n, $n)>=0) {

%o                 return $k;

%o             }

%o         }

%o         $k++;

%o     }

%o }

%o (Haskell)

%o import Data.List (isInfixOf, isPrefixOf)

%o a226219 n = head [k | k <- [2..],

%o                       isInfixOf (show n) (show (k*n)), not $ p10 k]

%o    where p10 = flip isPrefixOf ('1' : repeat '0') . show  :: Int -> Bool

%o -- _Reinhard Zumkeller_, May 31 2013

%Y Cf. A045537.

%K base,nonn

%O 0,1

%A _Paul Tek_, May 31 2013