A226219 Least k > 1 not a power of 10 such that n is a substring of k*n.

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, 5, 51, 101, 26, 79, 11, 101, 26, 101, 51, 21, 26, 101, 51, 87, 6, 59, 34, 101, 26, 21, 51, 74, 26, 51, 3, 69, 26, 29, 51, 21, 26, 101, 51, 27, 6, 92, 51, 26, 26, 21

Offset: 0

Author

Paul Tek, May 31 2013

Keywords

• base
• nonn

Links

• Paul Tek, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A045537.

Programs

Haskell

import Data.List (isInfixOf, isPrefixOf)
a226219 n = head [k | k <- [2..],
                      isInfixOf (show n) (show (k*n)), not $ p10 k]
   where p10 = flip isPrefixOf ('1' : repeat '0') . show  :: Int -> Bool
-- Reinhard Zumkeller, May 31 2013

Mathematica

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 *)

Perl

sub a {
    my $n = shift;
    my $k = 2;
    while (1) {
        if ($k !~ /^10+$/) {
            if (index($k*$n, $n)>=0) {
                return $k;
            }
        }
        $k++;
    }
}

Formula

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