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A356378
Main diagonal of the RILO variant of the array A035486; this is one of eight such sequences discussed in A007063.
2
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.
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
Sequence in context: A193725 A077952 A077975 * A258656 A112323 A102507
KEYWORD
nonn
AUTHOR
Clark Kimberling, Oct 21 2022
STATUS
approved