

A053300


Continued fraction for Pi/2.


7



1, 1, 1, 3, 31, 1, 145, 1, 4, 2, 8, 1, 6, 1, 2, 3, 1, 4, 1, 5, 1, 41, 1, 2, 3, 7, 1, 1, 1, 27, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 49, 2, 1, 4, 3, 6, 2, 1, 3, 3, 17, 1, 3, 2, 1, 6, 3, 1, 6, 26, 3, 1, 1, 3, 4, 3, 2, 14, 11, 1, 4, 1, 1, 5, 2, 8, 8, 2, 80, 1, 1, 22, 2, 11, 2, 1
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OFFSET

0,4


LINKS

Harry J. Smith, Table of n, a(n) for n = 0..20000
Michael A. Filaseta, Allen Stenger, D. Callan and Z. Franco, Solution to Problem 10640: When a Multiple of Pi/2 is Close to an Integer, Amer. Math. Monthly, 107 (2000), 177178.
I. Rosenholtz, Tangent sequences, world records, ..., Math. Mag., 72 (No. 5, 1999), 367376.
G. Xiao, Contfrac
Index entries for continued fractions for constants


EXAMPLE

1.57079632679489661923132169... = 1 + 1/(1 + 1/(1 + 1/(3 + 1/(31 + ...)))).  Harry J. Smith, May 31 2009


MATHEMATICA

ContinuedFraction[ Pi/2, 100 ]


PROG

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi/2); for (n=0, 20000, write("b053300.txt", n, " ", x[n+1])); } \\ Harry J. Smith, May 31 2009
(Magma) R:= RealField(); ContinuedFraction(Pi(R)/2); // G. C. Greubel, May 24 2018


CROSSREFS

Cf. A001203.
Cf. A019669 (decimal expansion).  Harry J. Smith, May 31 2009
Sequence in context: A145385 A059232 A068698 * A322777 A089281 A212729
Adjacent sequences: A053297 A053298 A053299 * A053301 A053302 A053303


KEYWORD

nonn,cofr


AUTHOR

N. J. A. Sloane, Mar 21 2000


STATUS

approved



