

A096444


Decimal expansion of (Pi  1)/2.


9



1, 0, 7, 0, 7, 9, 6, 3, 2, 6, 7, 9, 4, 8, 9, 6, 6, 1, 9, 2, 3, 1, 3, 2, 1, 6, 9, 1, 6, 3, 9, 7, 5, 1, 4, 4, 2, 0, 9, 8, 5, 8, 4, 6, 9, 9, 6, 8, 7, 5, 5, 2, 9, 1, 0, 4, 8, 7, 4, 7, 2, 2, 9, 6, 1, 5, 3, 9, 0, 8, 2, 0, 3, 1, 4, 3, 1, 0, 4, 4, 9, 9, 3, 1, 4, 0, 1, 7, 4, 1, 2, 6, 7, 1, 0, 5, 8, 5, 3, 3, 9, 9, 1, 0, 7
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..105.
I. Rosenholtz, Tangent sequences, world records, Pi, and the meaning of life: Some Applications of Number Theory to Calculus, Math. Mag., 72 (No. 5, 1999), 367376.
Jan W. H. Swanepoel, On a generalization of a theorem by Euler, Journal of Number Theory 149 (April 2015), pp. 4656.


FORMULA

Equals Sum_{k >= 1} sin(k)/k. (This follows from the identity x = Pi  2 Sum_{k >= 1} sin(kx)/k, as observed by Euler in 1744.)
Equals A019669 minus 1/2.  R. J. Mathar, Dec 15 2008
Equals Sum_{k >= 1} (sin(k)/k)^2. (Interestingly, Sum_{k >= 1} sin(k)/k = Sum_{k >= 1} (sin(k)/k)^2, a series whose terms sum to the sum of the square of each term.)  Dimitri Papadopoulos, Mar 11 2015


EXAMPLE

1.0707963267948966...


MATHEMATICA

RealDigits[(Pi  1)/2, 10, 105][[1]] (* Robert G. Wilson v, Aug 26 2004 *)


PROG

(PARI) (Pi1)/2 \\ Charles R Greathouse IV, Jan 30 2015
(MAGMA) pi:=Pi(RealField(110)); Reverse(Intseq(Floor(10^105*(pi1)/2))); // Vincenzo Librandi, Mar 12 2015


CROSSREFS

Cf. A096418.
Sequence in context: A216185 A202996 A019597 * A246918 A055957 A165090
Adjacent sequences: A096441 A096442 A096443 * A096445 A096446 A096447


KEYWORD

nonn,cons


AUTHOR

N. J. A. Sloane, Aug 16 2004


EXTENSIONS

More terms from Robert G. Wilson v, Aug 17 2004
Better definition from Eric W. Weisstein, Aug 18 2004


STATUS

approved



