A080511 Triangle whose n-th row contains the least set (ordered lexicographically) of n distinct positive integers whose arithmetic mean is an integer.

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, 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, 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

Offset: 1

Author

Amarnath Murthy, Mar 20 2003

Keywords

• nonn
• tabl

Comments

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

Examples

			Triangle starts:
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, 7, 12;
...
		

Crossrefs

Cf. A080512, A008619, A080504, A080508.

Programs

Maple

T:= proc(n) $1..n-1, `if`(irem(n, 2)=1, n, 3*n/2) end:
seq(T(n), n=1..20);  # Alois P. Heinz, Aug 29 2013

Mathematica

row[n_] := Append[Range[n - 1], If[OddQ[n], n, 3 n/2]];
Table[row[n], {n, 1, 20}] // Flatten (* Jean-François Alcover, May 21 2016 *)