A113595

[Hans Havermann]

> %I A113595
> %S A113595 12,12,12,12,45,12,56,56,45,90,0,1920
> %N A113595 Least multiple of n as a concatenation of two successive  
> natural numbers k and k+1, or 0 if no such number exists.
> %C A113595 Perhaps a(11) = 0. Subsidiary sequences: Least multiple  
> of n as a concatenation of r successive natural numbers k+1,...upto  
> k+r. 0 if no such numbers.
> %K A113595 base,more,nonn,new
> %O A113595 0,1
> %A A113595 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 07 2005

Assuming 'multiple' means >1 and the concatenation is left-to-right  
only, I get:

{12, 12, 12, 12, 45, 12, 56, 56, 45, 910, 1617, 1920, 78, 56, 45,  
1920, 34, 1314, 2223, 1920, 1617, 2728, 2829, 1920, 2425, 78, 3132,  
56, 3132, 1920, 2728, 1920, 1617, 3536, 910, 3132, 2627, 4142, 78,  
1920, 2829, 3738, 2021, 2728, 4950, 5152, 2021, 1920, 1617, 4950,  
5253, 3536, 3233, 3132, 4950, 5152, 2223, 3132, 6667, 1920, 3233,  
2728, 5859, 1920, 910, 4950, 6566, 3536, 2829, 910, 2627, 6768, 1314,  
6364, 4950, 7980, 1617, 6162, 6162, 1920, 8586, 6970, 2324, 7980,  
6970, 6364, 3132, 2728, 3738, 4950, 910, 5152, 5859, 6768, 7980,  
1920, 2425, 6566, 4950, 99100}

So, a(10) and a(11) were both wrong, I think. The "Perhaps a(11) =  
0." should have prevented the user from submitting more than 10 terms.

If we allow either left-to-right or right-to-left concatenations, I get:

{10, 10, 12, 12, 10, 12, 21, 32, 45, 910, 1617, 1716, 65, 56, 45, 32,  
34, 54, 76, 1920, 1617, 1716, 1817, 1920, 2425, 78, 54, 56, 87, 1110,  
2728, 1312, 1617, 3332, 910, 3132, 1110, 76, 78, 1920, 1312, 3738,  
2021, 1716, 4140, 4140, 2021, 1920, 98, 4950, 5049, 1716, 2120, 2322,  
4950, 5152, 2223, 2726, 5251, 1920, 2928, 2728, 5859, 1920, 910,  
1716, 6566, 3332, 2829, 910, 2627, 6768, 1314, 1110, 2625, 7372,  
1617, 1716, 1817, 1920, 7776, 1312, 2324, 7980, 1615, 2322, 3132,  
2728, 3738, 4140, 910, 4140, 3534, 2726, 1615, 1920, 2425, 3332,  
4950, 99100}