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
KEYWORD
nonn,tabf
AUTHOR
Boris Putievskiy, Dec 21 2012
STATUS
approved