A058651 Continued fraction for Pi + e.

5, 1, 6, 7, 3, 21, 2, 1, 2, 2, 1, 1, 2, 3, 3, 2, 5, 2, 1, 1, 1, 1, 3, 1, 8, 4, 4, 1, 1, 1, 1, 8, 1, 4, 1, 5, 1, 1, 1, 2, 4, 3, 2, 1, 1, 2, 1, 10, 1, 4, 1, 2, 1, 12, 1, 8, 2, 7, 39, 365, 2, 15, 2, 25, 1, 2, 5, 3, 3, 9, 3, 1, 1, 9, 1, 1, 47, 1, 1, 18, 1, 1, 2, 6, 1, 1, 1, 4, 1, 3, 1, 1, 1, 1, 4, 1, 6, 37

Offset: 0

Author

Avi Peretz (njk(AT)netvision.net.il), Dec 26 2000

Keywords

• nonn
• cofr
• easy

Comments

The question of the transcendence of the number Pi + e is still open.

Examples

			a(1) = 5 because Pi + e = 5.859874482048838473822930854632165381954416493075065395941912220031...
5.859874482048838473822930854... = 5 + 1/(1 + 1/(6 + 1/(7 + 1/(3 + ...)))). - _Harry J. Smith_, May 31 2009
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..19999
• G. Xiao, Contfrac
• Index entries for continued fractions for constants

Crossrefs

Cf. A001203, A003417.

Cf. A059742 (decimal expansion).

Programs

PARI

\p 500; contfrac(Pi+exp(1))

PARI

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi+exp(1)); for (n=1, 20000, write("b058651.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 31 2009

Extensions

More terms from Jason Earls, Jun 28 2001

Offset changed by Andrew Howroyd, Aug 04 2024