A172471 a(n) = floor(sqrt(2*n)).

0, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12

Offset: 0

Author

Vincenzo Librandi, Feb 04 2010

Keywords

• nonn
• easy

Comments

If k is even, k appears k+1 times; if k is odd, k appears k times. - N. J. A. Sloane, Jan 25 2021

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..20000 [First 10000 terms from Vincenzo Librandi]

Crossrefs

Cf. A000196, A003056, A103128, A005843.

Programs

Haskell

a172471 = a000196 . (* 2)  -- Reinhard Zumkeller, Feb 12 2012

Magma

[Floor(Sqrt(2*n)) : n in [0..80]];

Mathematica

Table[Floor[Sqrt[2n]],{n,0,80}]

PARI

a(n) = sqrtint(2*n); \\ Michel Marcus, May 23 2025

Formula

a(n) = A000196(2*n). - R. J. Mathar, Jul 06 2010