A356377 Main diagonal of the ROLI variant of the array A035486; this is one of eight such sequences discussed in A007063.

1, 3, 5, 4, 8, 6, 10, 15, 2, 9, 13, 26, 11, 12, 33, 34, 35, 29, 22, 37, 44, 48, 56, 39, 43, 54, 36, 16, 23, 25, 76, 81, 47, 30, 42, 14, 72, 38, 74, 71, 68, 92, 77, 46, 69, 94, 78, 128, 45, 110, 89, 73, 135, 90, 62, 115, 101, 104, 85, 153, 113, 158, 171, 172

Offset

1,2

Comments

Conjecture: every positive integer occurs exactly once.

Links

Table of n, a(n) for n=1..64.

Mathematica

len = 8; roli = Join[{{1}}, NestList[Join[#[[Riffle[Range[Length[#], (Length[#] + 3)/2, -1], Range[(Length[#] - 1)/2, 1, -1]]]],
     Range[#, # + 2] &[(3 Length[#] + 1)/2]] &, {2, 3, 4}, 200]];
s = Map[{#, Take[Flatten[Map[Take[#, {(Length[#] + 1)/2}] &, #]], 150] &[
      ToExpression[#]]} &, {"roli"}];
Last[First[s]]   (* A356377 *)
(* Peter J. C. Moses, Jul 26 2022 *)
(* The next program generates the ROLI array. *)
len = 8; roli = Join[{{1}}, NestList[Join[#[[Riffle[Range[Length[#], (Length[#] + 3)/2, -1], Range[(Length[#] - 1)/2, 1, -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[#]]]}]] &[roli]]
(* Peter J. C. Moses, Aug 02 2022 *)

Crossrefs

Cf. A007063, A035486.

Sequence in context: A069918 A361709 A200700 * A075380 A349374 A248497

Adjacent sequences: A356374 A356375 A356376 * A356378 A356379 A356380

Keyword

nonn

Author

Clark Kimberling, Oct 21 2022

Status

approved