A099188 a(n) = 2*ceiling(n/sqrt(2)).

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, 36, 38, 40, 40, 42, 44, 44, 46, 48, 50, 50, 52, 54, 54, 56, 58, 58, 60, 62, 64, 64, 66, 68, 68, 70, 72, 74, 74, 76, 78, 78, 80, 82, 84, 84, 86, 88, 88, 90, 92, 92, 94, 96, 98, 98, 100

Offset: 0

Author

David W. Wilson, Mar 26 2005

Keywords

• nonn
• easy

Comments

Conjecturally, length of shortest polygonal path from (0,0) to (n,n) with integer vertices and edges. This is true for n <= 10000.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Programs

Haskell

a099188 = (* 2) . a049474  -- Reinhard Zumkeller, Jul 03 2015

Magma

[2*Ceiling(n/Sqrt(2)): n in [0..100]]; // G. C. Greubel, Aug 17 2018

Mathematica

2Ceiling[Range[0,80]/Sqrt[2]] (* Harvey P. Dale, Dec 21 2011 *)

PARI

a(n)=if(n,2+2*sqrtint((n^2-1)\2)) \\ Charles R Greathouse IV, Jan 10 2013

Formula

a(n) = 2*A049474(n).