A003077 Decimal expansion of 22/7 - Pi.
0, 0, 1, 2, 6, 4, 4, 8, 9, 2, 6, 7, 3, 4, 9, 6, 1, 8, 6, 8, 0, 2, 1, 3, 7, 5, 9, 5, 7, 7, 6, 3, 9, 9, 7, 2, 9, 4, 5, 6, 8, 7, 7, 4, 3, 4, 8, 2, 0, 3, 7, 0, 3, 6, 1, 6, 7, 9, 1, 2, 5, 5, 0, 5, 4, 9, 3, 2, 6, 4, 5, 0, 8, 5, 6, 6, 4, 8, 1, 4, 4, 2, 2, 9, 1, 0, 8, 0, 3, 1, 8, 0, 0, 7, 4, 0, 0, 7, 4, 8
Offset: 0
Examples
0.001264489267349618680213759577639972945687743482037036167912550549326450856...
References
- Alf van der Poorten, Notes on Fermat's Last Theorem, Wiley, 1996, p. 15.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..10000
- MathOverflow, Source and context of 22/7-Pi = Integral_{0..1} (x-x^2)^4/(1+x^2) dx ?
- Paul J. Nahin, Inside interesting integrals, Undergrad. Lecture Notes in Physics, Springer (2020), (1.7.1)
- Anthony Sofo, Euler related binomial sums, Indian J. Pure Appl. Math. 50 (1) (2019) 149-160
- Eric Weisstein's MathWorld, Pi
- Wikipedia, Pi
- Index entries for transcendental numbers
Programs
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Magma
m:=152; [0,0] cat Reverse(Intseq(Floor(10^m*(22/7 - Pi(RealField(m+5)))))); // G. C. Greubel, Nov 03 2022
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Mathematica
Join[{0, 0}, RealDigits[22/7-Pi, 10, 98][[1]]] (* Jean-François Alcover, May 24 2013 *) -
PARI
22/7-Pi \\ Charles R Greathouse IV, Sep 30 2022
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SageMath
(22/7 - pi).n(digits=150).nextbelow() # G. C. Greubel, Nov 03 2022
Formula
22/7 - Pi = Integral_{x=0..1} x^4*(1-x)^4/(1+x^2). - M. F. Hasler, Oct 24 2011
Equals 60*Sum_{n>=1} 1/[(4*n^2-1)*(16*n^2-1)*(16*n^2-9)] . [Sofo] - R. J. Mathar, Jun 21 2024