A217570 Numbers n such that floor(sqrt(n)) = floor(n/(floor(sqrt(n))-1))-1.

9, 16, 17, 25, 26, 27, 36, 37, 38, 39, 49, 50, 51, 52, 53, 64, 65, 66, 67, 68, 69, 81, 82, 83, 84, 85, 86, 87, 100, 101, 102, 103, 104, 105, 106, 107, 121, 122, 123, 124, 125, 126, 127, 128, 129, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 169, 170, 171, 172, 173

Offset

1,1

Comments

The sequence consists of numbers n^2+k, 0<=k<=n-3, n=3,4,5,... - M. F. Hasler, Oct 09 2012

One of four sequences given by classifying natural numbers according to the value of floor(sqrt(n)). See the paper in Link lines and A005563, A217571, A217575. - Takumi Sato, Oct 09 2012

Links

Table of n, a(n) for n=1..60.

Takumi Sato, Classification of Natural Numbers

Example

As a triangle (see the first comment) this begins:
9;
16, 17;
25, 26, 27;
36, 37, 38, 39;
49, 50, 51, 52, 53;
64, 65, 66, 67, 68, 69;
81, 82, 83, 84, 85, 86, 87;
100, 101, 102, 103, 104, 105, 106, 107; etc.
[Bruno Berselli, Oct 12 2012]

Prog

(Visual Basic in Excel)
Sub A217570()
Dim x As Long, n As Long, y As Long, i As Long
x = InputBox("Count to")
For n = 2 To x
y = Int(Sqr(n))
If y = Int(n / y) Then GoTo L1
GoTo L2
L1: If y = Int(n / (y - 1)) - 1 Then
i = i + 1
Cells(i, 1) = n
End If
L2: Next n
End Sub
(PARI) is_A217570(n)={ n>3 & n\(n=sqrtint(n)-1)==n+2}  \\ - M. F. Hasler, Oct 09 2012

Crossrefs

Cf. A005563, A217571, A217575.

Sequence in context: A201266 A231977 A269563 * A274188 A335437 A034040

Adjacent sequences: A217567 A217568 A217569 * A217571 A217572 A217573

Keyword

nonn

Author

Takumi Sato, Oct 07 2012

Status

approved