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.)

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

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: A354367 A194071 A194104 * A108644 A194011 A370698

Adjacent sequences: A277676 A277677 A277678 * A277680 A277681 A277682

Keyword

nonn,easy

Author

Clark Kimberling, Nov 14 2016

Status

approved