A097285 Contains exactly once every pair (i,j) of distinct positive integers.

1, 2, 1, 3, 2, 3, 1, 4, 2, 4, 3, 4, 1, 5, 2, 5, 3, 5, 4, 5, 1, 6, 2, 6, 3, 6, 4, 6, 5, 6, 1, 7, 2, 7, 3, 7, 4, 7, 5, 7, 6, 7, 1, 8, 2, 8, 3, 8, 4, 8, 5, 8, 6, 8, 7, 8, 1, 9, 2, 9, 3, 9, 4, 9, 5, 9, 6, 9, 7, 9, 8, 9, 1, 10, 2, 10, 3, 10, 4, 10, 5, 10, 6, 10, 7, 10, 8, 10, 9, 10, 1, 11, 2, 11, 3, 11, 4, 11, 5

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

Juxtapose segments: 1 2, then 1 3 2 3, then 1 4 2 4 3 4. General segment is 1 n 2 n ... n-1 n, followed by 1, so that clearly, every i<j and every i>j is uniquely present.

Maple

A097285:= proc(n) local k, j;
   k:= floor(sqrt(n-3/4)-1/2);
   j:= floor((n-k^2-k)/2);
   if n::odd then j+1 else k+2 fi
end proc;
seq(A097285(n), n=1..100); # Robert Israel, May 08 2014

Mathematica

S = {1, 2}; Do[S = Join[S, Riffle[Range[n-1], n], {n}], {n, 3, 12}];
S (* Jean-François Alcover, Apr 11 2019 *)

Crossrefs

Cf. A097286.

Sequence in context: A379631 A307314 A057940 * A372917 A057432 A374741

Adjacent sequences: A097282 A097283 A097284 * A097286 A097287 A097288

Keyword

nonn

Author

Clark Kimberling, Aug 05 2004

Status

approved