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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

%I #14 Aug 04 2021 10:06:34

%S 1,2,7,64,227,2182,24901,27904,519413,9103082,8410247,207985216,

%T 1106853941,3134651098,85885292267,2808012157952,2944757946677,

%U 402260886146,14238994069127,14850593365952,632726700580207,26229300849325726,25294817897063581,1230908174013784832

%N 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 + ... .

%C 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.

%D 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.

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

%o (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)),", "))};

%o a346781(47)

%Y The corresponding denominators are A025547.

%Y Cf. A091337, A196525.

%K nonn,frac

%O 1,2

%A _Hugo Pfoertner_, Aug 03 2021

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Last modified August 9 20:51 EDT 2024. Contains 375044 sequences. (Running on oeis4.)