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A235382 a(n) = smallest number of unit squares required to enclose n units of area. 5

%I

%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, C. Winterer, <a href="http://whaleconjecture.wordpress.com/">WhaleConjecture</a>.

%H E. Daring, I. Guadarrama, S. Sprague, 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

%Y Cf. A027434, A027709, A232091.

%K nonn,easy

%O 0,1

%A _L. Edson Jeffery_, Jan 08 2014

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Last modified March 29 17:23 EDT 2020. Contains 333116 sequences. (Running on oeis4.)