A080511 - OEIS

%I #14 May 21 2016 03:04:43

%S 1,1,3,1,2,3,1,2,3,6,1,2,3,4,5,1,2,3,4,5,9,1,2,3,4,5,6,7,1,2,3,4,5,6,

%T 7,12,1,2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,8,9,15,1,2,3,4,5,6,7,8,9,10,11,

%U 1,2,3,4,5,6,7,8,9,10,11,18,1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,3,4,5,6,7,8,9,10,11,12,13,21

%N Triangle whose n-th row contains the least set (ordered lexicographically) of n distinct positive integers whose arithmetic mean is an integer.

%C The n-th row is {1,2,...,n-1,x}, where x=n if n is odd, x=3n/2 if n is even.

%e Triangle starts:

%e 1;

%e 1, 3;

%e 1, 2, 3;

%e 1, 2, 3, 6;

%e 1, 2, 3, 4, 5;

%e 1, 2, 3, 4, 5, 9;

%e 1, 2, 3, 4, 5, 6, 7;

%e 1, 2, 3, 4, 5, 6, 7, 12;

%e ...

%p T:= proc(n) $1..n-1, `if`(irem(n, 2)=1, n, 3*n/2) end:

%p seq(T(n), n=1..20);  # _Alois P. Heinz_, Aug 29 2013

%t row[n_] := Append[Range[n - 1], If[OddQ[n], n, 3 n/2]];

%t Table[row[n], {n, 1, 20}] // Flatten (* _Jean-François Alcover_, May 21 2016 *)

%Y Cf. A080512, A008619, A080504, A080508.

%K nonn,tabl

%O 1,3

%A _Amarnath Murthy_, Mar 20 2003