A356376 Main diagonal of the LORO variant of the array A035486; this is one of eight such sequences discussed in A007063.

1, 3, 5, 6, 4, 11, 12, 9, 13, 15, 23, 7, 27, 16, 24, 25, 34, 36, 19, 14, 50, 41, 10, 40, 60, 32, 43, 35, 26, 20, 38, 63, 79, 81, 57, 44, 74, 80, 65, 72, 107, 28, 53, 93, 76, 66, 114, 56, 129, 55, 119, 47, 103, 125, 85, 39, 45, 141, 106, 77, 98, 137, 109, 33

Offset: 1

Author

Clark Kimberling, Oct 21 2022

Keywords

• nonn

Comments

Conjecture: every positive integer except 2 occurs exactly once.

Crossrefs

Cf. A007063, A035486.

Programs

Mathematica

loro = Join[{{1}}, NestList[Join[#[[Riffle[Range[1, (Length[#] - 1)/2],
      Range[Length[#], (Length[#] + 3)/2, -1]]]],
      Range[#, # + 2] &[(3 Length[#] + 1)/2]] &, {2, 3, 4}, 200]];
s = Map[{#, Take[Flatten[Map[Take[#, {(Length[#] + 1)/2}] &, #]], 150] &[
      ToExpression[#]]} &, {"loro"}]; u = Last[First[s]]
(* Peter J. C. Moses, Jul 26 2022 *)
(* The next program generates the LORO array. *)
len = 8; loro = Join[{{1}}, NestList[Join[#[[Riffle[Range[1, (Length[#] - 1)/2],
     Range[Length[#], (Length[#] + 3)/2, -1]]]],
     Range[#, # + 2] &[(3 Length[#] + 1)/2]] &, {2, 3, 4}, len]];
Grid[Map[Flatten, Transpose[{#, Range[3 Range[Length[#]] - 1,
       4 (Length[#] - 2) - 1 + Range[Length[#]]]}]] &[loro]]
(* Peter J. C. Moses, Aug 02 2022 *)