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
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A097286.
Programs
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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
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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.