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A068028 Decimal expansion of 22/7. 15
3, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This is an approximation to Pi. It is accurate to 0.04025%.
Consider the recurring part of 22/7 and the sequences R(i) = 2, 1, 4, 2, 3, 0, 2, ... and Q(i) = 1, 4, 2, 8, 5, 7, 1, .... For i > 0, let X(i) = 10*R(i) + Q(i). Then Q(i+1) = floor(X(i)/Y); R(i+1) = X(i) - Y*Q(i+1); here Y=5; X(0)=X=7. Note 1/7 = 7/49 = X/(10*Y-1). Similar comment holds elsewhere. If we consider the sequences R(i) = 3, 2, 3, 5, 5, 1, 4, 0, 6, 4, 6, 3, 4, 3, 1, 1, 5, 2, 6, 0, 2, 0, 3, ... and Q(i) = A021027, we have X=3; Y=7 (attributed to Vedic literature). - K.V.Iyer, Jun 16 2010, Jun 18 2010
The sequence of convergents of the continued fraction of Pi begins [3, 22/7, 333/106, 355/113, 103993/33102, ...]. 22/7 is the second convergent. The summation 240*Sum_{n >= 1} 1/((4*n+1)*(4*n+2)*(4*n+3)*(4*n+5)(4*n+6)*(4*n+7)) = 22/7 - Pi shows that 22/7 is an over-approximation to Pi. - Peter Bala, Oct 12 2021
LINKS
D. Castellanos, The ubiquitous pi, Math. Mag., 61 (1988), 67-98 and 148-163. - N. J. A. Sloane, Mar 24 2012
D. P. Dalzell, On 22/7, J. London Math. Soc. 19, 133-134, 1944.
Dale Winham, Facts about Pi
FORMULA
a(0)=3, a(n) = floor(714285/10^(5-(n mod 6)). - Sascha Kurz, Mar 23 2002.
Equals 100*A021018 - 4 = 3 + A020806. - R. J. Mathar, Sep 30 2008
For n>1 a(n) = A020806(n-2) (note offset=0 in A020806 and offset=1 in A068028). - Zak Seidov, Mar 26 2015
G.f.: x*(3-2*x+3*x^2+x^3+4*x^4)/((1-x)*(1+x)*(1-x+x^2)). - Vincenzo Librandi, Mar 27 2015
MATHEMATICA
CoefficientList[Series[(3 - 2 x + 3 x^2 + x^3 + 4 x^4) / ((1 - x) (1 + x) (1 - x + x^2)), {x, 0, 100}], x] (* Vincenzo Librandi, Mar 27 2015 *)
Join[{3}, LinearRecurrence[{1, 0, -1, 1}, {1, 4, 2, 8}, 104]] (* Ray Chandler, Aug 26 2015 *)
RealDigits[22/7, 10, 120][[1]] (* Harvey P. Dale, Oct 04 2021 *)
PROG
(Magma) I:=[3, 1, 4, 2, 8]; [n le 5 select I[n] else Self(n-1)-Self(n-3)+Self(n-4): n in [1..100]]; // Vincenzo Librandi, Mar 27 2015
(PARI) a(n)=22/7. \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
Sequence in context: A365434 A115659 A067060 * A240058 A275896 A340754
KEYWORD
easy,nonn,cons
AUTHOR
Nenad Radakovic, Mar 22 2002.
EXTENSIONS
More terms from Sascha Kurz, Mar 23 2002
Alternative to broken link added by R. J. Mathar, Jun 18 2010
STATUS
approved

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)