A235382 a(n) = smallest number of unit squares required to enclose n units of area.

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.)

Kival Ngaokrajang, Illustration of initial terms

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

Cf. A027434, A027709, A232091.

Sequence in context: A310972 A246357 A265378 * A287201 A310973 A310974

Adjacent sequences: A235379 A235380 A235381 * A235383 A235384 A235385

Keyword

nonn,easy

Author

L. Edson Jeffery, Jan 08 2014

Status

approved