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A194195 First inverse function (numbers of rows) for pairing function A060734 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The sequence is the second inverse function (numbers of columns) for pairing function A060736.
LINKS
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
Sequence in context: A210870 A104726 A364954 * A164999 A292030 A162909
KEYWORD
nonn,tabf
AUTHOR
Boris Putievskiy, Dec 21 2012
STATUS
approved

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Last modified June 12 11:40 EDT 2024. Contains 373331 sequences. (Running on oeis4.)