cp's OEIS Frontend

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

%I A217570 #49 Dec 23 2024 21:57:23
%S A217570 9,16,17,25,26,27,36,37,38,39,49,50,51,52,53,64,65,66,67,68,69,81,82,
%T A217570 83,84,85,86,87,100,101,102,103,104,105,106,107,121,122,123,124,125,
%U A217570 126,127,128,129,144,145,146,147,148,149,150,151,152,153,169,170,171,172,173
%N A217570 Numbers n such that floor(sqrt(n)) = floor(n/(floor(sqrt(n))-1))-1.
%C A217570 The sequence consists of numbers n^2+k, 0<=k<=n-3, n=3,4,5,... - _M. F. Hasler_, Oct 09 2012
%C A217570 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
%H A217570 Robert Israel, <a href="/A217570/b217570.txt">Table of n, a(n) for n = 1..10000</a>
%H A217570 Takumi Sato, <a href="http://vixra.org/abs/1210.0025">Classification of Natural Numbers</a>
%e A217570 As a triangle (see the first comment) this begins:
%e A217570 9;
%e A217570 16, 17;
%e A217570 25, 26, 27;
%e A217570 36, 37, 38, 39;
%e A217570 49, 50, 51, 52, 53;
%e A217570 64, 65, 66, 67, 68, 69;
%e A217570 81, 82, 83, 84, 85, 86, 87;
%e A217570 100, 101, 102, 103, 104, 105, 106, 107; etc.
%e A217570 [_Bruno Berselli_, Oct 12 2012]
%p A217570 seq($n^2 .. n^2 + n - 3, n=3..20); # _Robert Israel_, Dec 23 2024
%o A217570 (Visual Basic in Excel)
%o A217570 Sub A217570()
%o A217570 Dim x As Long, n As Long, y As Long, i As Long
%o A217570 x = InputBox("Count to")
%o A217570 For n = 2 To x
%o A217570 y = Int(Sqr(n))
%o A217570 If y = Int(n / y) Then GoTo L1
%o A217570 GoTo L2
%o A217570 L1: If y = Int(n / (y - 1)) - 1 Then
%o A217570 i = i + 1
%o A217570 Cells(i, 1) = n
%o A217570 End If
%o A217570 L2: Next n
%o A217570 End Sub
%o A217570 (PARI) is_A217570(n)={ n>3 & n\(n=sqrtint(n)-1)==n+2}  \\ - _M. F. Hasler_, Oct 09 2012
%Y A217570 Cf. A005563, A217571, A217575.
%K A217570 nonn
%O A217570 1,1
%A A217570 _Takumi Sato_, Oct 07 2012