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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
1, 2, 7, 64, 227, 2182, 24901, 27904, 519413, 9103082, 8410247, 207985216, 1106853941, 3134651098, 85885292267, 2808012157952, 2944757946677, 402260886146, 14238994069127, 14850593365952, 632726700580207, 26229300849325726, 25294817897063581, 1230908174013784832 (list; graph; refs; listen; history; text; internal format)
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
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.
Sequence in context: A100523 A181030 A006506 * A011821 A366705 A117263
KEYWORD
nonn,frac
AUTHOR
Hugo Pfoertner, Aug 03 2021
STATUS
approved

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Last modified July 25 00:10 EDT 2024. Contains 374585 sequences. (Running on oeis4.)