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%I #5 Dec 05 2013 19:55:18
%S 10,210,321,432,543210,654,7,8765432,987654321,109876543210,11,
%T 1211109876,13,14131211109876,151413121110,1615141312,171615,
%U 181716151413121110,19181716,20,21,2221201918171615141312,23
%N 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.
%C 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, ...
%e a(7) = 7 the corresponding k = 0, a(2) =210, k=2. a(4) = 432, k = 2.
%t 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}]
%Y Cf. A069860, A069861, A069862.
%K base,nonn,less
%O 1,1
%A _Amarnath Murthy_, Apr 18 2002
%E Edited by _Robert G. Wilson v_, Apr 22 2002
%E Edited by _T. D. Noe_, Apr 09 2009