

A228295


The 'Honeycomb' or 'Beehive' sequence: a(n) = ceiling(12^(1/4)*n).


0



0, 2, 4, 6, 8, 10, 12, 14, 15, 17, 19, 21, 23, 25, 27, 28, 30, 32, 34, 36, 38, 40, 41, 43, 45, 47, 49, 51, 53, 54, 56, 58, 60, 62, 64, 66, 68, 69, 71, 73, 75, 77, 79, 81, 82, 84, 86, 88, 90, 92, 94, 95, 97, 99, 101, 103, 105, 107, 108, 110, 112, 114, 116, 118, 120, 121
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OFFSET

0,2


COMMENTS

Sequence gives the approximate perimeter of n hexagons of unit area, assuming each side is shared with another hexagon.
This could form a Beatty sequence.
This is not A195125, although they match until 37th term and never after the 1000th term.


LINKS

Table of n, a(n) for n=0..65.
ABC Shop, The Code with description
American Scientist, The Soap Film: An Analogue Computer
American Scientist, Foams and Honeycombs
The BBC Productions, The Code; see in particular Behind the Beehive  The Code  Episode 2
Thomas C. Hales, The Honeycomb Conjecture, arXiv:math/9906042 [math.MG], 19992002.
Marcus P. F. du Sautoy, The Code, a DVD produced by Athena, 2011.
Scienceray, Is Bee a Mathematician?  mathematics in nature.


FORMULA

a(n) = ceiling( 12^(1/4) * n ).


MATHEMATICA

f[n_] := Ceiling[ Sqrt[ Sqrt[12]]*n]; Array[f, 66, 0]


CROSSREFS

Cf. A011009.
Sequence in context: A324847 A302696 A195125 * A184592 A247427 A316837
Adjacent sequences: A228292 A228293 A228294 * A228296 A228297 A228298


KEYWORD

nonn


AUTHOR

Marcus du Sautoy and Robert G. Wilson v, Aug 19 2013


STATUS

approved



