OFFSET
1,1
COMMENTS
The extremal examples were described by Y. S. Kupitz in 1991.
REFERENCES
Y. S. Kupitz, "On the maximal number of appearances of the minimal distance among n points in the plane", in Intuitive geometry: Proceedings of the 3rd international conference held in Szeged, Hungary, 1991; Amsterdam: North-Holland: Colloq. Math. Soc. Janos Bolyai. 63, 217-244.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = 3*n + ceiling(sqrt(12*n - 3)). - H. Harborth
2*a(n) - A135711(n) = 6n. - Tanya Khovanova, Mar 07 2008
MATHEMATICA
Table[3*n + Ceiling[Sqrt[12*n - 3]], {n, 1, 25}] (* G. C. Greubel, Oct 29 2016 *)
PROG
(Magma) [3*n+Ceiling(Sqrt(12*n-3)): n in [1..65]]; // Vincenzo Librandi, Oct 30 2016
(PARI) a(n) = 3*n + ceil(sqrt(12*n-3)); \\ Michel Marcus, Oct 30 2016
(Python)
from math import isqrt
def A135708(n): return 3*n+1+isqrt(12*n-4) # Chai Wah Wu, Jul 28 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, based on an email from Sascha Kurz, Mar 05 2008
STATUS
approved