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%I #18 Oct 18 2022 01:31:51
%S 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,
%T 11,13,13,13,13,13,13,13,13,13,13,13,13,15,15,15,15,15,15,15,15,15,15,
%U 15,15,15,15,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17
%N 2n+1 appears 2n times.
%F a(n) = 2*floor(sqrt(n)+1/2)+1. - _Mikael Aaltonen_, Jan 14 2015
%F From _Robert Israel_, Jan 14 2015: (Start)
%F 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.
%F a(2n) = a(2n-1) = 2*A002024(n)+1.
%F a(n) = A001670(n)+1.
%F (End)
%p seq(2*n+1 $ 2*n, n=1..10); # _Robert Israel_, Jan 14 2015
%o (Python)
%o from math import isqrt
%o def A130829(n): return 1|((m:=isqrt(n))+int((n-m*(m+1)<<2)>=1)<<1) # _Chai Wah Wu_, Oct 17 2022
%Y Cf. A001670, A002024, A003057.
%K nonn
%O 1,1
%A _Paul Curtz_, Jul 17 2007
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