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Begin with n and place (n-1) on the least significant side, place (n-2) on the most significant side and so on until a 1 is placed.
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%I #5 Dec 05 2013 19:56:35

%S 1,21,132,2431,13542,246531,1357642,24687531,135798642,24681097531,

%T 1357911108642,246810121197531,13579111312108642,2468101214131197531,

%U 135791113151412108642,24681012141615131197531

%N Begin with n and place (n-1) on the least significant side, place (n-2) on the most significant side and so on until a 1 is placed.

%e a(6)= 246531, the steps are 6 -> 65 -> 465 -> 4653 -> 24653 -> 246531.

%t f[n_] := Block[{j = 1, k = n - 1, d = IntegerDigits[n]}, While[k > 0, If[ EvenQ[j], d = Join[ IntegerDigits[k], d], d = Join[d, IntegerDigits[k]]]; j++; k-- ]; FromDigits[d]]; Table[ f[n], {n, 17}]

%Y Cf. A089370.

%K base,easy,nonn

%O 1,2

%A _Amarnath Murthy_, Nov 08 2003

%E More terms from _Robert G. Wilson v_, Nov 08 2003