A053300 Continued fraction for Pi/2.

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

Offset: 0

Author

N. J. A. Sloane, Mar 21 2000

Keywords

• nonn
• cofr

Examples

			1.57079632679489661923132169... = 1 + 1/(1 + 1/(1 + 1/(3 + 1/(31 + ...)))). - _Harry J. Smith_, May 31 2009
		

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), 177-178.
• I. Rosenholtz, Tangent sequences, world records, ..., Math. Mag., 72 (No. 5, 1999), 367-376.
• G. Xiao, Contfrac
• Index entries for continued fractions for constants

Crossrefs

Cf. A001203.

Cf. A019669 (decimal expansion). - Harry J. Smith, May 31 2009

Programs

Magma

R:= RealField(); ContinuedFraction(Pi(R)/2); // G. C. Greubel, May 24 2018

Mathematica

ContinuedFraction[ Pi/2, 100 ]

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