A060018 a(n) = floor(2*sqrt(n-2)).
0, 2, 2, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16
Offset: 2
Links
- Harry J. Smith, Table of n, a(n) for n = 2..1000
- J. R. Griggs, Spanning subset sums for finite Abelian groups, Discrete Math., 229 (2001), 89-99.
- Matthew Hyatt, Marina Skyers, On the Increases of the Sequence floor(k*sqrt(n)), Electronic Journal of Combinatorial Number Theory, Volume 15 #A17.
Crossrefs
Cf. A060019.
Programs
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Magma
[Floor(2*Sqrt(n-2)): n in [2..100]]; // Vincenzo Librandi, Dec 09 2015
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Mathematica
Floor[2*Sqrt[Range[2,80]-2]] (* Harvey P. Dale, Aug 19 2015 *)
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PARI
{ default(realprecision, 100); for (n=2, 1000, write("b060018.txt", n, " ", floor(2*sqrt(n - 2))); ) } \\ Harry J. Smith, Jul 01 2009 -
PARI
a(n)=sqrtint(4*n-8) \\ Charles R Greathouse IV, Aug 23 2011
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Python
from math import isqrt def A060018(n): return isqrt(n-2<<2) # Chai Wah Wu, Jun 06 2025
Formula
a(n) = floor(2*sqrt(n-2)) = floor(sqrt(4*n-8)). - Charles R Greathouse IV, Nov 26 2015
G.f.: (Sum_{k>=1} x^(k^2+2) + x^(k^2-k+3))/(1-x)
= (x^2 * (Theta3(x)-1) + x^(11/4) * Theta2(x))/(2-2*x) where Theta2 and Theta3 are Jacobi theta functions. - Robert Israel, Dec 09 2015
a(n) = A000194(n-2) + A000196(n-2) = floor(sqrt(n-2)+1/2) + floor(sqrt(n-2)). - Ridouane Oudra, Jun 07 2019