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 A068028 Decimal expansion of 22/7. 13
 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 Index entries for linear recurrences with constant coefficients, signature (1, 0, -1, 1). 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 Cf. A068079, A068089, A002485, A002486, A046965, A046947. Sequence in context: A274531 A115659 A067060 * A240058 A275896 A340754 Adjacent sequences:  A068025 A068026 A068027 * A068029 A068030 A068031 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 August 8 10:04 EDT 2022. Contains 356009 sequences. (Running on oeis4.)