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

1,1

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, ...

Links

Table of n, a(n) for n=1..23.

Example

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

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}]

Crossrefs

Cf. A069860, A069861, A069862.

Sequence in context: A211107 A335673 A215555 * A160476 A067642 A334537

Adjacent sequences: A069860 A069861 A069862 * A069864 A069865 A069866

Keyword

base,nonn,less

Author

Amarnath Murthy, Apr 18 2002

Extensions

Edited by Robert G. Wilson v, Apr 22 2002

Edited by T. D. Noe, Apr 09 2009

Status

approved