|
%I #21 Jan 28 2023 10:37:42
%S 0,2,4,6,6,8,10,10,12,14,16,16,18,20,20,22,24,26,26,28,30,30,32,34,34,
%T 36,38,40,40,42,44,44,46,48,50,50,52,54,54,56,58,58,60,62,64,64,66,68,
%U 68,70,72,74,74,76,78,78,80,82,84,84,86,88,88,90,92,92,94,96,98,98,100
%N a(n) = 2*ceiling(n/sqrt(2)).
%C Conjecturally, length of shortest polygonal path from (0,0) to (n,n) with integer vertices and edges. This is true for n <= 10000.
%H Reinhard Zumkeller, <a href="/A099188/b099188.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = 2*A049474(n).
%t 2Ceiling[Range[0,80]/Sqrt[2]] (* _Harvey P. Dale_, Dec 21 2011 *)
%o (PARI) a(n)=if(n,2+2*sqrtint((n^2-1)\2)) \\ _Charles R Greathouse IV_, Jan 10 2013
%o (Haskell)
%o a099188 = (* 2) . a049474 -- _Reinhard Zumkeller_, Jul 03 2015
%o (Magma) [2*Ceiling(n/Sqrt(2)): n in [0..100]]; // _G. C. Greubel_, Aug 17 2018
%K nonn,easy
%O 0,2
%A _David W. Wilson_, Mar 26 2005
|
