A153192 Numbers such that the numerator of floor(sqrt(n))/n, when reduced to its lowest terms, is equal to 2.
5, 7, 18, 22, 39, 45, 68, 76, 105, 115, 150, 162, 203, 217, 264, 280, 333, 351, 410, 430, 495, 517, 588, 612, 689, 715, 798, 826, 915, 945, 1040, 1072, 1173, 1207, 1314, 1350, 1463, 1501, 1620, 1660, 1785, 1827, 1958
Offset: 1
Examples
22 has 4 square numbers below it and 4/22=2/11. 76 has 8 square numbers below it and 8/76=2/19.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
- Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
Crossrefs
Cf. A153194.
Programs
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Mathematica
LinearRecurrence[{1,2,-2,-1,1},{5,7,18,22,39},50] (* Harvey P. Dale, Sep 23 2022 *) -
PARI
isok(n) = numerator(sqrtint(n)/n) == 2 \\ Michel Marcus, Aug 05 2013
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PARI
for(n=1,9,print1(4*n^2+n", "4*n^2+3*n", ")) \\ Charles R Greathouse IV, Aug 05 2013
Formula
From Colin Barker, Mar 28 2014: (Start)
a(n) = (2*n+3)*(2*n-(-1)^n+1)/4.
a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^2+2*x+5) / ((x-1)^3*(x+1)^2). (End).
Extensions
Definition simplified and more terms added by Michel Marcus, Aug 05 2013
Comments