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

1,3

Comments

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

Links

Boris Putievskiy, Rows n = 1..140 of triangle, flattened

Boris Putievskiy, Transformations Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012.

Formula

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

Example

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").

Mathematica

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

Prog

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

Crossrefs

Cf. A060734, A060736, A220603, A220604.

Sequence in context: A131730 A029335 A029257 * A165927 A127830 A371275

Adjacent sequences: A194255 A194256 A194257 * A194259 A194260 A194261

Keyword

nonn,tabf

Author

Boris Putievskiy, Dec 21 2012

Status

approved