A130829 2n+1 appears 2n times.

3, 3, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17

Offset

1,1

Links

Table of n, a(n) for n=1..72.

Formula

a(n) = 2*floor(sqrt(n)+1/2)+1. - Mikael Aaltonen, Jan 14 2015

From Robert Israel, Jan 14 2015: (Start)

G.f.: x/(1-x)*(1+2*sum(m>=0, x^(m*(m+1))) = x/(1-x)*(1+x^(-1/4)*theta_2(0,x)) where theta_2 is the second Jacobi theta function.

a(2n) = a(2n-1) = 2*A002024(n)+1.

a(n) = A001670(n)+1.

(End)

Maple

seq(2*n+1 $ 2*n, n=1..10); # Robert Israel, Jan 14 2015

Prog

(Python)
from math import isqrt
def A130829(n): return 1|((m:=isqrt(n))+int((n-m*(m+1)<<2)>=1)<<1) # Chai Wah Wu, Oct 17 2022

Crossrefs

Cf. A001670, A002024, A003057.

Sequence in context: A349530 A251549 A129972 * A196386 A035158 A196172

Adjacent sequences: A130826 A130827 A130828 * A130830 A130831 A130832

Keyword

nonn

Author

Paul Curtz, Jul 17 2007

Status

approved