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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

Table of n, a(n) for n=1..105.

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 sequences related to the number 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.)