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%I #36 Sep 08 2022 08:46:06
%S 4,8,10,12,12,14,14,16,16,16,18,18,18,20,20,20,20,22,22,22,22,24,24,
%T 24,24,24,26,26,26,26,26,28,28,28,28,28,28,30,30,30,30,30,30,32,32,32,
%U 32,32,32,32,34,34,34,34,34,34,34,36,36,36,36,36
%N a(n) = smallest number of unit squares required to enclose n units of area.
%C Result attributed to the students Daring, et al., in the links section.
%H Charles R Greathouse IV, <a href="/A235382/b235382.txt">Table of n, a(n) for n = 0..10000</a>
%H E. Daring, I. Guadarrama, S. Sprague, and C. Winterer, <a href="http://whaleconjecture.wordpress.com/">WhaleConjecture</a>.
%H E. Daring, I. Guadarrama, S. Sprague, and C. Winterer, <a href="http://whaleconjecture.files.wordpress.com/2012/07/the-new-whale-conjecture-casey-edit-2.pdf">The Whale Theorem</a>. (PDF contains incomplete proof.)
%H Kival Ngaokrajang, <a href="/A235382/a235382_1.pdf">Illustration of initial terms</a>
%F a(n) = 2*ceiling(2*sqrt(n)) + 4.
%F a(n) = A027709(n) + 4.
%F a(n) = 2*A027434(n) + 4, n>0.
%t Table[2 Ceiling[2 Sqrt[n]] + 4, {n, 0, 49}] (* _Michael De Vlieger_, Jul 21 2016 *)
%o (PARI) a(n)=if(n,2*sqrtint(4*n-1)+6,4) \\ _Charles R Greathouse IV_, Jan 09 2014
%o (Magma) [2*Ceiling(2*Sqrt(n))+4: n in [0..70]]; // _Vincenzo Librandi_, Jul 27 2016
%o (Python)
%o from math import isqrt
%o def A235382(n): return 3+isqrt((n<<2)-1)<<1 if n else 4 # _Chai Wah Wu_, Jul 28 2022
%Y Cf. A027434, A027709, A232091.
%K nonn,easy
%O 0,1
%A _L. Edson Jeffery_, Jan 08 2014
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