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%I #7 Dec 03 2016 11:52:02
%S 1,3,2,7,4,5,13,6,9,8,17,10,11,14,15,23,16,19,12,25,18,33,26,27,20,21,
%T 24,31,49,32,39,22,29,28,35,34,53,36,43,30,37,40,41,50,51,59,52,55,42,
%U 45,38,61,44,67,54,85,68,69,62,63,46,47,56,57,60,77,95
%N Start with 1,2,3,4,5,6,.... For n >=1, remove the first n terms and reverse the remaining terms n+1 at a time. Concatenate the terms removed. (See the example.)
%C This is a permutation of the natural numbers, with inverse permutation A277680.
%H Clark Kimberling, <a href="/A277679/b277679.txt">Table of n, a(n) for n = 1..10000</a>
%e Remove 1 from A000027, leaving 2,3,4,5,6,7,8,...; reverse these 2 at a time, leaving 3,2,5,4,7,6,9,8,... Remove the first 2 terms and reverse the rest 3 at a time, leaving 7,4,5,8,9,6,13,10,11,14,15,12,... Remove the first 3 terms, and so on. The removed terms, taken in order, are 1,3,2,7,4,5,...
%t x = Range[500];
%t NestWhile[# + 1 &, 1, (t = 1/2 # (1 + #);
%t x = Flatten[{Take[x, t],
%t Map[Reverse, Partition[Drop[x, t], # + 1]]}];
%t Length[x] > t) &]; x (* A277679 *)
%t Take[Ordering[#],Position[Differences[Sort[#]],Except[1]][[2]][[1]]]&[x] (* A277680 *) (* _Peter J. C. Moses_, Nov 13 2016 *)
%Y Cf. A000027, A277680, A007062, A057030.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Nov 14 2016
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