A055972 Continued fraction for the number 1 + 1/(e + 1/(e^2 + 1/(e^3 + 1/(e^4 +...)))).

1, 2, 1, 5, 1, 3, 1, 2, 1, 57, 1, 5, 3, 1, 2847, 7, 1, 1, 3, 4, 4, 8, 1, 1, 48, 1, 1, 2, 1, 2, 81, 1, 2, 3, 12, 1, 1, 1, 5, 1, 3, 1, 6, 1, 5, 3, 2, 1, 2, 1, 3, 1, 2, 1, 1, 5, 6, 96, 1, 1, 1, 1, 1, 3, 1, 19

Offset: 0

Author

Leroy Quet, Jul 19 2000

Keywords

• cofr
• nonn

Examples

			1.3505436043221124180470983246597483686...
1.350543604322112418047098324... = 1 + 1/(2 + 1/(1 + 1/(5 + 1/(1 + ...)))). - _Harry J. Smith_, May 03 2009
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..2000
• G. Xiao, Contfrac
• Index entries for continued fractions for constants

Crossrefs

Cf. A100609 Decimal expansion. - Harry J. Smith, May 03 2009

Programs

PARI

f(n)= { x=0; for (i=1, n, x=1/(exp(1+n-i) + x)); 1+x } { allocatemem(932245000); default(realprecision, 2100); y=1.0; n=70; x=f(n); while(x!=y, y=x; n=n+1; x=f(n);); c=contfrac(x); for (n=1, 2001, write("b055972.txt", n-1, " ", c[n])); } \\ Harry J. Smith, May 03 2009