

A277679


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.)


2



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, 24, 31, 49, 32, 39, 22, 29, 28, 35, 34, 53, 36, 43, 30, 37, 40, 41, 50, 51, 59, 52, 55, 42, 45, 38, 61, 44, 67, 54, 85, 68, 69, 62, 63, 46, 47, 56, 57, 60, 77, 95
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OFFSET

1,2


COMMENTS

This is a permutation of the natural numbers, with inverse permutation A277680.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000


EXAMPLE

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,...


MATHEMATICA

x = Range[500];
NestWhile[# + 1 &, 1, (t = 1/2 # (1 + #);
x = Flatten[{Take[x, t],
Map[Reverse, Partition[Drop[x, t], # + 1]]}];
Length[x] > t) &]; x (* A277679 *)
Take[Ordering[#], Position[Differences[Sort[#]], Except[1]][[2]][[1]]]&[x] (* A277680 *) (* Peter J. C. Moses, Nov 13 2016 *)


CROSSREFS

Cf. A000027, A277680, A007062, A057030.
Sequence in context: A154438 A194071 A194104 * A108644 A194011 A303763
Adjacent sequences: A277676 A277677 A277678 * A277680 A277681 A277682


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Nov 14 2016


STATUS

approved



