A296768 Initially let b(i)=i for all i > 0. On the k-th pass, exchange b(k+1) with b(b(k+1) + b(k)). The sequence is the limit of these sequences as k goes to infinity.

1, 3, 5, 9, 11, 17, 24, 32, 36, 46, 48, 60, 73, 87, 102, 118, 124, 142, 161, 181, 202, 224, 247, 254, 279, 305, 332, 360, 389, 419, 450, 458, 491, 525, 560, 564, 601, 639, 678, 718, 759, 801, 844, 888, 933, 943, 990, 992, 1041, 1091, 1142, 1194, 1247, 1301, 1356, 1412, 1469, 1527, 1586, 1598, 1659, 1721, 1784, 1848, 1913, 1979, 2046

Offset

1,2

Links

Table of n, a(n) for n=1..67.

Example

Initially the sequence {b[n]} is {1,2,3,4,5,...};
on the first pass, exchange b(2) with b(b(2) + b(1)) to give {1,3,2,4,5,...};
on the second pass, exchange b(3) with b(b(3) + b(2)), that is, exchange b(3) with b(5) to give {1,3,5,4,2,...}.

Mathematica

For[n = 0, n <= 1000, n++, a[n] = n];
iend = 48;
For[k = 2, k <= iend, k++, t = Table[a[n], {n, 1, iend}]; Print[k, t];
   temp = a[k]; index = a[a[k] + a[k - 1]]; a[k] = index;
  a[index] = temp];
(* Second program: *)
With[{nn = 67}, Take[#, nn] &@ Fold[ReplacePart[#1, {#2 + 1 -> #1[[Total@ #1[[#2 ;; #2 + 1]] ]], #1[[Total@ #1[[#2 ;; #2 + 1]] ]] -> #1[[#2 + 1]] } ] &, Range[nn^2], Range@ nn] ] (* Michael De Vlieger, Dec 20 2017 *)

Crossrefs

Sequence in context: A007952 A145819 A317827 * A302596 A230721 A094509

Adjacent sequences: A296765 A296766 A296767 * A296769 A296770 A296771

Keyword

nonn

Author

David S. Newman, Dec 19 2017

Status

approved