cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A135708 Minimal total number of edges in a polyhex consisting of n hexagonal cells.

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%I A135708 #20 Sep 08 2022 08:45:32
%S A135708 6,11,15,19,23,27,30,34,38,41,45,48,52,55,59,62,66,69,72,76,79,83,86,
%T A135708 89,93,96,99,103,106,109,113,116,119,123,126,129,132,136,139,142,146,
%U A135708 149,152,155,159,162,165,168,172,175,178,181,185,188,191,194,198,201,204,207,210
%N A135708 Minimal total number of edges in a polyhex consisting of n hexagonal cells.
%C A135708 The extremal examples were described by Y. S. Kupitz in 1991.
%D A135708 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.
%H A135708 G. C. Greubel, <a href="/A135708/b135708.txt">Table of n, a(n) for n = 1..1000</a>
%F A135708 a(n) = 3*n + ceiling(sqrt(12*n - 3)). - H. Harborth
%F A135708 2*a(n) - A135711(n) = 6n. - _Tanya Khovanova_, Mar 07 2008
%t A135708 Table[3*n + Ceiling[Sqrt[12*n - 3]], {n,1,25}] (* _G. C. Greubel_, Oct 29 2016 *)
%o A135708 (Magma) [3*n+Ceiling(Sqrt(12*n-3)): n in [1..65]]; // _Vincenzo Librandi_, Oct 30 2016
%o A135708 (PARI) a(n) = 3*n + ceil(sqrt(12*n-3)); \\ _Michel Marcus_, Oct 30 2016
%o A135708 (Python)
%o A135708 from math import isqrt
%o A135708 def A135708(n): return 3*n+1+isqrt(12*n-4) # _Chai Wah Wu_, Jul 28 2022
%Y A135708 Cf. A135711.
%K A135708 nonn
%O A135708 1,1
%A A135708 _N. J. A. Sloane_, based on an email from _Sascha Kurz_, Mar 05 2008