A188723 Continued fraction of (Pi + sqrt(4 + Pi^2))/2.

3, 2, 3, 4, 2, 3, 1, 1, 105, 1, 2, 1, 13, 5, 16, 1, 44, 1, 1, 4, 2, 1, 2, 3, 100, 4, 1, 1, 18, 4, 2, 2, 2, 8, 2, 5, 2, 2, 3, 7, 184, 1, 8, 6, 2, 6, 2, 1, 5, 1, 38, 1, 2, 1, 1, 1, 4, 2, 6, 2, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 2, 1, 2, 3, 8, 1, 1, 2, 1, 3, 1, 2, 1, 10, 1, 6, 1, 3, 1, 1, 1, 1, 2, 2, 1, 7, 1, 11, 1, 6, 1, 2, 13, 35, 1, 5, 2, 2, 1, 1, 2, 8, 2, 6, 2, 3, 1, 1, 2, 5

Offset

0,1

Comments

Continued fraction of the constant in A188722.

Links

Table of n, a(n) for n=0..119.

Maple

Digits := 100 ;
(Pi+sqrt(4+Pi^2))/2 ;
evalf(%) ;
numtheory[cfrac](%, 40, 'quotients') ; # R. J. Mathar, Apr 11 2011

Mathematica

r = Pi; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]

Crossrefs

Cf. A000796, A188640, A188722 (decimal expansion).

Sequence in context: A214435 A215926 A007888 * A341890 A077178 A267376

Adjacent sequences: A188720 A188721 A188722 * A188724 A188725 A188726

Keyword

nonn,cofr

Author

Clark Kimberling, Apr 09 2011

Extensions

Offset changed by Andrew Howroyd, Jul 07 2024

Status

approved