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)
import math
def a(n):
t=math.isqrt(n-1)+1
return min(t, t**2-n+1)
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Boris Putievskiy, Dec 21 2012
STATUS
approved
