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

1,2

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.

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.

Links

Table of n, a(n) for n=1..24.

Example

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

Prog

(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)

Crossrefs

The corresponding denominators are A025547.

Cf. A091337, A196525.

Sequence in context: A100523 A181030 A006506 * A011821 A366705 A117263

Adjacent sequences: A346778 A346779 A346780 * A346782 A346783 A346784

Keyword

nonn,frac

Author

Hugo Pfoertner, Aug 03 2021

Status

approved