A234398 Distribution of the natural numbers using the sequences family mentioned in the comments.

1, 2, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 6, 1, 2, 6, 2, 2, 6, 3, 2, 6, 4, 2, 6, 5, 2, 6, 6, 2, 6, 7, 2, 6, 8, 2, 6, 9, 2, 6, 10, 2, 6, 10, 1, 2, 6, 10, 2, 2, 6, 10, 3, 2, 6, 10, 4, 2, 6, 10, 5, 2, 6, 10, 6, 2, 6, 10, 7

Offset: 1

Author

Paul Curtz, Dec 25 2013

Keywords

• nonn
• uned

Comments

Based on A016825=2,6,10,..., the family is

N16(1)=1, followed by 2's =A040000,

N16(2)=1,2,3,4,5, followed by 6's =A101272,

N16(3)=1,2,3,4,5,6,7,8,9, followed by 10's, not in the OEIS,

N16(4)=1,2,3,4,5,6,7,8,9,10,11,12,13, followed by 14's, idem.

The N16(n) gives the successive columns beginning at row 1, 3, 9, 19, ... =A058331.

Sum of every row: n =A000027.

Note that with only N16(1),

1,

2,

2, 1,

2, 2,

2, 2, 1,

2, 2, 2,

2, 2, 2, 1,

2, 2, 2, 2,

2, 2, 2, 2, 1, etc

is A169695(n+1).

A169695(n) corresponds to A028310.

Examples

			1,
2,
2, 1,
2, 2,
2, 3,
2, 4,
2, 5,
2, 6,
2, 6, 1,
2, 6, 2,
2, 6, 3,
2, 6, 4, etc.
		

Crossrefs

Cf. A173642.