A346781 a(n) is the numerator of the sum of the first n terms of 1 - 1/3 - 1/5 + 1/7 + 1/9 - 1/11 - 1/13 + ... .

1, 2, 7, 64, 227, 2182, 24901, 27904, 519413, 9103082, 8410247, 207985216, 1106853941, 3134651098, 85885292267, 2808012157952, 2944757946677, 402260886146, 14238994069127, 14850593365952, 632726700580207, 26229300849325726, 25294817897063581, 1230908174013784832

Offset: 1

Author

Hugo Pfoertner, Aug 03 2021

Keywords

• nonn
• frac

Comments

The limit for n->oo of the sum 1 - 1/3 - 1/5 + 1/7 + ... is log(1+sqrt(2))/sqrt(2) (A196525). See there for more information.

Examples

			1, 2/3, 7/15, 64/105, 227/315, 2182/3465, 24901/45045, 27904/45045, ...
		

References

• Barry Mazur, Chapter IV.1 Algebraic Numbers, page 316, in The Princeton Companion to Mathematics, ed. Timothy Gowers, Princeton University Press, Princeton and Oxford, 2008.

Crossrefs

The corresponding denominators are A025547.

Cf. A091337, A196525.

Programs

PARI

a346781(limit)={my(s=0,b(n)=1/(n*sign(4-(n+2)%8)));forstep(k=1,limit,2,print1(numerator(s+=b(k)),", "))};
a346781(47)