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A228295
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The 'Honeycomb' or 'Beehive' sequence: a(n) = ceiling(12^(1/4)*n).
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1
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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
(list;
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history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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Marcus P. F. du Sautoy, The Code, a DVD produced by Athena, 2011.
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FORMULA
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a(n) = ceiling( 12^(1/4) * n ).
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MATHEMATICA
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f[n_] := Ceiling[ Sqrt[ Sqrt[12]]*n]; Array[f, 66, 0]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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