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

1,2

Links

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

Example

1.35054360432211241804709832465974836866146733205836404665602916628...

Mathematica

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

Prog

(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

Crossrefs

Cf. A001113.

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

Sequence in context: A307209 A243967 A144541 * A104866 A165723 A257407

Adjacent sequences: A100606 A100607 A100608 * A100610 A100611 A100612

Keyword

cons,nonn

Author

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

Extensions

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

Status

approved