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

Author

L. Edson Jeffery, Jan 08 2014

Keywords

• nonn
• easy

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

Crossrefs

Cf. A027434, A027709, A232091.

Programs

Magma

[2*Ceiling(2*Sqrt(n))+4: n in [0..70]]; // Vincenzo Librandi, Jul 27 2016

Mathematica

Table[2 Ceiling[2 Sqrt[n]] + 4, {n, 0, 49}] (* Michael De Vlieger, Jul 21 2016 *)

PARI

a(n)=if(n,2*sqrtint(4*n-1)+6,4) \\ Charles R Greathouse IV, Jan 09 2014

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

Formula

a(n) = 2*ceiling(2*sqrt(n)) + 4.

a(n) = A027709(n) + 4.

a(n) = 2*A027434(n) + 4, n>0.