A153194 Numbers such that the numerator of floor(sqrt(n))/n, when reduced to its lowest terms, is equal to 3.
10, 11, 13, 14, 38, 40, 44, 46, 84, 87, 93, 96, 148, 152, 160, 164, 230, 235, 245, 250, 330, 336, 348, 354, 448, 455, 469, 476, 584, 592, 608, 616, 738, 747, 765, 774, 910, 920, 940, 950, 1100, 1111, 1133, 1144, 1308, 1320, 1344, 1356
Offset: 1
Examples
For 38, there are 6 squares below it and 6/38=3/19. For 164 there are 12 squares below it and 12/164=3/41.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,2,-2,0,0,-1,1).
Crossrefs
Cf. A153192.
Programs
-
Mathematica
CoefficientList[Series[(10 + x + 2 x^2 + x^3 + 4 x^4)/((1 - x) (1 - x^4)^2), {x, 0, 60}], x] (* Vincenzo Librandi, Mar 29 2014 *) -
PARI
isok(n) = numerator(sqrtint(n)/n) == 3 \\ Michel Marcus, Aug 05 2013
-
PARI
Vec(-x*(4*x^4+x^3+2*x^2+x+10)/((x-1)^3*(x+1)^2*(x^2+1)^2) + O(x^100)) \\ Colin Barker, Mar 28 2014
Formula
G.f.: -x*(4*x^4+x^3+2*x^2+x+10) / ((x-1)^3*(x+1)^2*(x^2+1)^2). - Colin Barker, Mar 28 2014
G.f.: x * (10 + x + 2*x^2 + x^3 + 4*x^4) / ((1 - x) * (1 - x^4)^2). - Michael Somos, Mar 28 2014
a(n+4) = 2*a(n) - a(n-4) + 18 if n>0. - Michael Somos, Mar 28 2014
Extensions
Edited and more terms added by Michel Marcus, Aug 05 2013
Comments