A194195 First inverse function (numbers of rows) for pairing function A060734

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

Offset

1,2

Comments

The sequence is the second inverse function (numbers of columns) 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; t^2 - n + 1}, where t=floor(sqrt(n-1))+1.

Example

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

Mathematica

f[n_]:=Module[{t=Floor[Sqrt[n-1]]+1}, Min[t, t^2-n+1]]; Array[f, 80] (* Harvey P. Dale, Dec 31 2012 *)

Prog

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

Crossrefs

Cf. A060734, A060736, A220603, A220604

Sequence in context: A210870 A104726 A364954 * A164999 A292030 A162909

Adjacent sequences: A194192 A194193 A194194 * A194196 A194197 A194198

Keyword

nonn,tabf

Author

Boris Putievskiy, Dec 21 2012

Status

approved