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Second inverse function (numbers of columns) for pairing function A060734.
2

%I #19 Apr 28 2016 12:42:20

%S 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,

%T 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,

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

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

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

%H Boris Putievskiy, <a href="/A194258/b194258.txt">Rows n = 1..140 of triangle, flattened</a>

%H Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a> arXiv:1212.2732 [math.CO], 2012.

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

%e The start of the sequence as triangle array read by rows:

%e 1;

%e 1,2,2;

%e 1,2,3,3,3;

%e 1,2,3,4,4,4,4;

%e . . .

%e Row number k contains 2k-1 numbers 1,2,...k-1,k,k,...k (k times repetition "k").

%t Flatten[Table[Join[Range[n-1],Table[n,{n}]],{n,10}]] (* _Harvey P. Dale_, Jun 23 2013 *)

%o (Python)

%o t=int(math.sqrt(n-1)) +1

%o j=min(t,n-(t-1)**2)

%Y Cf. A060734, A060736, A220603, A220604.

%K nonn,tabf

%O 1,3

%A _Boris Putievskiy_, Dec 21 2012