A228295 The 'Honeycomb' or 'Beehive' sequence: a(n) = ceiling(12^(1/4)*n).

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

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], 1999-2002.

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]

Prog

(Python)
from sympy import integer_nthroot
def A228295(n): return 0 if n == 0 else 1+integer_nthroot(12*n**4, 4)[0] # Chai Wah Wu, Mar 17 2021

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