A069863 a(n) is the shortest concatenation of two or more decreasing consecutive numbers (n)(n-1)...(0) such that n divides a(n), or n if there is no such concatenation.

10, 210, 321, 432, 543210, 654, 7, 8765432, 987654321, 109876543210, 11, 1211109876, 13, 14131211109876, 151413121110, 1615141312, 171615, 181716151413121110, 19181716, 20, 21, 2221201918171615141312, 23

Offset: 1

Author

Amarnath Murthy, Apr 18 2002

Keywords

• base
• nonn
• less

Comments

a(n) = n for the following values of n: 7, 11, 13, 20, 21, 23, 25, 26, 29, 31, 37, 38, 39, 50, 52, 53, 58, 59, 62, 63, 65, 67, 71, 74, 81, 82, 85, 89, 91, 92, 95, 97, 100, 101, 106, 115, 116, 118, 130, 133, 145, 146, 152, 159, 169, 173, 175, 178, 182, 184, 185, 195, 196, 200, 212, 213, 214, 215, 217, 220, 221, 224, 227, 229, 230, 232, 235, 236, 239, 243, 250, ...

Examples

			a(7) = 7 the corresponding k = 0, a(2) =210, k=2. a(4) = 432, k = 2.
		

Crossrefs

Cf. A069860, A069861, A069862.

Programs

Mathematica

f[n_] := Block[{j = n, k = n - 1}, While[j = ToExpression[ StringJoin[ ToString[j], ToString[k]]]; !IntegerQ[j/n] && k > -1, k-- ]; If[k == -1, Return[n], Return[j]]]; Table[f[n], {n, 1, 30}]

Extensions

Edited by Robert G. Wilson v, Apr 22 2002

Edited by T. D. Noe, Apr 09 2009