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

%I A194258 #19 Apr 28 2016 12:42:20
%S A194258 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 A194258 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 A194258 5,6,7,8,9,9,9,9,9,9,9,9,9,1,2,3,4,5,6
%N A194258 Second inverse function (numbers of columns) for pairing function A060734.
%C A194258 The  sequence is the first inverse function (numbers of rows) for pairing function A060736.
%H A194258 Boris Putievskiy, <a href="/A194258/b194258.txt">Rows n = 1..140 of triangle, flattened</a>
%H A194258 Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a> arXiv:1212.2732 [math.CO], 2012.
%F A194258 a(n) = min{t; n - (t - 1)^2}, where t=floor(sqrt(n-1))+1.
%e A194258 The start of the sequence as triangle array read by rows:
%e A194258 1;
%e A194258 1,2,2;
%e A194258 1,2,3,3,3;
%e A194258 1,2,3,4,4,4,4;
%e A194258 . . .
%e A194258 Row number k contains 2k-1 numbers 1,2,...k-1,k,k,...k (k times repetition "k").
%t A194258 Flatten[Table[Join[Range[n-1],Table[n,{n}]],{n,10}]] (* _Harvey P. Dale_, Jun 23 2013 *)
%o A194258 (Python)
%o A194258 t=int(math.sqrt(n-1)) +1
%o A194258 j=min(t,n-(t-1)**2)
%Y A194258 Cf. A060734, A060736, A220603, A220604.
%K A194258 nonn,tabf
%O A194258 1,3
%A A194258 _Boris Putievskiy_, Dec 21 2012