A100609 Decimal expansion of the constant whose continued fraction representation is [e^0; e^1, e^2, e^3, e^4, ...] where e is A001113 and the exponents cycle through all nonnegative integers.

1, 3, 5, 0, 5, 4, 3, 6, 0, 4, 3, 2, 2, 1, 1, 2, 4, 1, 8, 0, 4, 7, 0, 9, 8, 3, 2, 4, 6, 5, 9, 7, 4, 8, 3, 6, 8, 6, 6, 1, 4, 6, 7, 3, 3, 2, 0, 5, 8, 3, 6, 4, 0, 4, 6, 6, 5, 6, 0, 2, 9, 1, 6, 6, 2, 8, 0, 9, 4, 7, 1, 9, 0, 4, 4, 1, 2, 4, 5, 8, 4, 5, 3, 8, 1, 5, 9, 0, 7, 8, 9, 4, 6, 5, 2, 5, 1, 9, 2, 4, 2, 6, 6, 0, 9

Offset: 1

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 01 2004

Keywords

• cons
• nonn

Examples

			1.35054360432211241804709832465974836866146733205836404665602916628...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A001113.

Cf. A055972 Continued fraction. - Harry J. Smith, May 03 2009

Programs

Mathematica

N[FromContinuedFraction[Table[E^k, {k, 0, 25}]], 111]

PARI

f(n)= { x=0; for (i=1, n, x=1/(exp(1+n-i) + x)); 1+x } { default(realprecision, 2080); y=1.0; n=70; x=f(n); while(x!=y, y=x; n=n+1; x=f(n);); for (m=1, 2000, d=floor(x); x=(x-d)*10; write("b100609.txt", m, " ", d)); } \\ Harry J. Smith, May 03 2009

Extensions

Fixed my PARI program, had -n numbers Harry J. Smith, May 19 2009