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A194258 Second inverse function (numbers of columns) for pairing function A060734. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A176816

Adjacent sequences:  A194255 A194256 A194257 * A194259 A194260 A194261

KEYWORD

nonn,tabf

AUTHOR

Boris Putievskiy, Dec 21 2012

STATUS

approved

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Last modified October 16 06:14 EDT 2021. Contains 348040 sequences. (Running on oeis4.)