A103128 a(n) = floor(sqrt(2n-1)).

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

Offset

1,3

Comments

n appears 2 * ceiling(n/2) times.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

From Robert Israel, Sep 12 2016: (Start)

a(n+1) = a(n)+1 for n in A007590, otherwise a(n+1) = a(n).

G.f.: x*Theta3(x^2)/(2*(1-x)) + sqrt(x)*Theta2(x^2)/(2*(1-x)) - x/(2*(1-x)), where Theta2 and Theta3 are Jacobi Theta functions. (End)

Maple

seq(floor(sqrt(2*n-1)), n=1..100); # Robert Israel, Sep 12 2016

Mathematica

Table[Floor[Sqrt[2n-1]], {n, 100}] (* Mohammad K. Azarian, Jun 15 2016 *)

Prog

(Haskell)
a103128 = a000196 . (subtract 1) . (* 2)
-- Reinhard Zumkeller, Feb 12 2012
(Python)
from math import isqrt
def A103128(n): return isqrt((n<<1)-1) # Chai Wah Wu, Oct 29 2025

Crossrefs

Cf. A172471, A000196, A005408, A007590.

Sequence in context: A106457 A331852 A379771 * A156080 A334233 A271058

Adjacent sequences: A103125 A103126 A103127 * A103129 A103130 A103131

Keyword

easy,nonn

Author

Giovanni Teofilatto, Mar 17 2005

Extensions

Edited by Franklin T. Adams-Watters, Apr 20 2010

New name from Wesley Ivan Hurt, Nov 26 2020

Status

approved