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
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
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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