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

Author

Clark Kimberling, Aug 05 2004

Keywords

• nonn

Links

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

Crossrefs

Cf. A097286.

Programs

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 *)

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 ij is uniquely present.