A356378 Main diagonal of the RILO variant of the array A035486; this is one of eight such sequences discussed in A007063.

1, 3, 5, 2, 10, 9, 15, 8, 20, 19, 7, 21, 31, 6, 25, 14, 42, 24, 16, 28, 53, 39, 33, 12, 23, 63, 18, 65, 76, 41, 62, 47, 64, 74, 59, 83, 99, 58, 98, 30, 60, 109, 50, 66, 122, 78, 91, 84, 100, 90, 129, 113, 49, 108, 56, 75, 71, 70, 13, 132, 169, 27, 149, 43

Offset: 1

Author

Clark Kimberling, Oct 21 2022

Keywords

• nonn

Comments

Conjecture: every positive integer occurs exactly once.

Crossrefs

Cf. A007063, A035486.

Programs

Mathematica

rilo = Join[{{1}}, NestList[Join[#[[Riffle[Range[(Length[#] + 3)/2, Length[#]],          Range[1, (Length[#] - 1)/2, 1]]]], Range[#, # + 2] &[(3 Length[#] + 1)/2]] &, {2, 3, 4}, 200]]; (* A356378 *)
s = Map[{#, Take[Flatten[Map[Take[#, {(Length[#] + 1)/2}] &, #]], 150] &[
      ToExpression[#]]} &, {"rilo"}];
Last[First[s]]   (* A356378 *)
(* Peter J. C. Moses,Jul 26 2022 *)
(* The next program generates the RILO array. *)
len = 8; rilo = Join[{{1}}, NestList[Join[#[[Riffle[Range[(Length[#] + 3)/2, Length[#]],
     Range[1, (Length[#] - 1)/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[#]]]}]] &[rilo]]
(* Peter J. C. Moses, Aug 02 2022 *)