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

1,3

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.

Links

Table of n, a(n) for n=1..105.

Example

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;
...

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 *)

Crossrefs

Cf. A080512, A008619, A080504, A080508.

Sequence in context: A167373 A079722 A079723 * A132399 A287616 A371101

Adjacent sequences: A080508 A080509 A080510 * A080512 A080513 A080514

Keyword

nonn,tabl

Author

Amarnath Murthy, Mar 20 2003

Status

approved