A384738 Decimal expansion of 3*log(2)/4 - Pi/8.
1, 2, 7, 1, 6, 1, 3, 0, 3, 7, 2, 1, 2, 3, 4, 8, 2, 7, 2, 5, 5, 0, 9, 3, 6, 6, 8, 1, 8, 3, 6, 9, 4, 5, 6, 5, 5, 3, 1, 9, 7, 8, 9, 2, 5, 8, 4, 8, 3, 0, 3, 2, 1, 2, 9, 6, 8, 6, 4, 1, 9, 3, 3, 0, 8, 1, 5, 6, 8, 1, 6, 5, 6, 9, 1, 4, 9, 4, 9, 1, 1, 8, 7, 5, 8, 9, 3
Offset: 0
Examples
0.12716130372123482725509366818369456553197892584830...
Links
- Jason Bard, Table of n, a(n) for n = 0..9999
- Steve Chow (Blackpenredpen), Not telescoping: series of 1/(4n-1)-1/(4n) (2019), YouTube video.
- Michael I. Shamos, A catalog of the real numbers, (2007). See p. 166.
Programs
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Mathematica
RealDigits[3/4*Log[2] - Pi/8, 10, 140][[1]]
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PARI
3*log(2)/4 - Pi/8 \\ Amiram Eldar, Jun 09 2025
Formula
Equals Sum_{k>=1} (1/(4k-1) - (1/4k)).
Equals Sum_{k>=2} zeta(k)/4^k.
Equals Integral_{x=1..oo} 1/(x^4+x^3+x^2+x) dx.
Equals A100046/2. - Amiram Eldar, Jun 09 2025
Comments