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A235382
a(n) = smallest number of unit squares required to enclose n units of area.
7
4, 8, 10, 12, 12, 14, 14, 16, 16, 16, 18, 18, 18, 20, 20, 20, 20, 22, 22, 22, 22, 24, 24, 24, 24, 24, 26, 26, 26, 26, 26, 28, 28, 28, 28, 28, 28, 30, 30, 30, 30, 30, 30, 32, 32, 32, 32, 32, 32, 32, 34, 34, 34, 34, 34, 34, 34, 36, 36, 36, 36, 36
OFFSET
0,1
COMMENTS
Result attributed to the students Daring, et al., in the links section.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 0..10000
E. Daring, I. Guadarrama, S. Sprague, and C. Winterer, WhaleConjecture.
E. Daring, I. Guadarrama, S. Sprague, and C. Winterer, The Whale Theorem. (PDF contains incomplete proof.)
FORMULA
a(n) = 2*ceiling(2*sqrt(n)) + 4.
a(n) = A027709(n) + 4.
a(n) = 2*A027434(n) + 4, n>0.
MATHEMATICA
Table[2 Ceiling[2 Sqrt[n]] + 4, {n, 0, 49}] (* Michael De Vlieger, Jul 21 2016 *)
PROG
(PARI) a(n)=if(n, 2*sqrtint(4*n-1)+6, 4) \\ Charles R Greathouse IV, Jan 09 2014
(Magma) [2*Ceiling(2*Sqrt(n))+4: n in [0..70]]; // Vincenzo Librandi, Jul 27 2016
(Python)
from math import isqrt
def A235382(n): return 3+isqrt((n<<2)-1)<<1 if n else 4 # Chai Wah Wu, Jul 28 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
L. Edson Jeffery, Jan 08 2014
STATUS
approved