A194258 Second inverse function (numbers of columns) for pairing function A060734.

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

Offset: 1

Author

Boris Putievskiy, Dec 21 2012

Keywords

• nonn
• tabf

Comments

The sequence is the first inverse function (numbers of rows) for pairing function A060736.

Examples

			The start of the sequence as triangle array read by rows:
1;
1,2,2;
1,2,3,3,3;
1,2,3,4,4,4,4;
. . .
Row number k contains 2k-1 numbers 1,2,...k-1,k,k,...k (k times repetition "k").
		

Links

• Boris Putievskiy, Rows n = 1..140 of triangle, flattened
• Boris Putievskiy, Transformations Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012.

Crossrefs

Cf. A060734, A060736, A220603, A220604.

Programs

Mathematica

Flatten[Table[Join[Range[n-1],Table[n,{n}]],{n,10}]] (* Harvey P. Dale, Jun 23 2013 *)

Python

t=int(math.sqrt(n-1)) +1
j=min(t,n-(t-1)**2)

Formula

a(n) = min{t; n - (t - 1)^2}, where t=floor(sqrt(n-1))+1.