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

1,2

Comments

Conjecture: every positive integer occurs exactly once.

Links

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

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 *)

Crossrefs

Cf. A007063, A035486.

Sequence in context: A193725 A077952 A077975 * A258656 A112323 A102507

Adjacent sequences: A356375 A356376 A356377 * A356379 A356380 A356381

Keyword

nonn

Author

Clark Kimberling, Oct 21 2022

Status

approved