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.
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
KEYWORD
nonn,frac
AUTHOR
Hugo Pfoertner, Aug 03 2021
STATUS
approved