OFFSET
1,2
COMMENTS
Observation: if b(k) denotes the sequence of all elements of the continued fraction for c, b(k) = 4095 if k==6 or 19 (mod 24); b(k) = 4722366482869645213695 if k==12 or 37 (mod 48); .... If b(k) is not congruent to 5 (mod 10), it seems that b(k) = 1,2,3 or 4 only.
Conjecture: a(3*2^n) = -1 + 2^[(n+1)((n+2)!) ]. - Ralf Stephan, May 17 2005
The conjecture follows from the theorem in Shallit's paper. The continued fraction has a "folded" overall structure. - Georg Fischer, Aug 29 2022
LINKS
Rick L. Shepherd, Table of n, a(n) for n = 1..47
Jeffrey O. Shallit, Simple Continued Fractions for Some Irrational Numbers II, J. Number Theory 14 (1982), 228-231.
Rick L. Shepherd, Table of n, a(n) for n = 1..383 (has larger terms than b-files support)
FORMULA
c=1.2656250596046447753906250000000000007... = A076187.
PROG
(PARI)
{allocatemem(220000000);
default(realprecision, 1000000);
contfrac(suminf(k=0, 1/(2^(k!))))}
CROSSREFS
KEYWORD
cofr,nonn
AUTHOR
Benoit Cloitre, Nov 02 2002
EXTENSIONS
More terms from Ralf Stephan, May 17 2005
b-file, a-file, PARI program, and corrected conjecture by Rick L. Shepherd, Jun 07 2013
STATUS
approved