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

1,2

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.

Links

Table of n, a(n) for n=1..72.

Example

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.

Sequence in context: A302490 A316841 A000003 * A168208 A333003 A352072

Adjacent sequences: A234395 A234396 A234397 * A234399 A234400 A234401

Keyword

nonn,uned

Author

Paul Curtz, Dec 25 2013

Status

approved