OFFSET
0,1
COMMENTS
Number of terms in the n-th partial sum of the Fermat number reciprocals.
LINKS
Daniel Duverney, Irrationality of Fast Converging Series of Rational Numbers, J. Math. Sci. Univ. Tokyo, 8 (2001), 275-316.
N. J. A. Sloane and James A. Sellers, On non-squashing partitions, Discrete Mathematics, Vol. 294, No. 3 (2005), pp. 259-274; arXiv preprint, arXiv:math/0312418 [math.CO], 2003.
EXAMPLE
The partial sum for n = 3 (four terms) is: 1/3 + 1/5 + 1/17 + 1/257 = 39062/65535 expressed in continued fraction gives: {0,1,1,2,9,1,2,1,1,2,2,1,2,1,5} that has 15 elements so: a(3) = 15.
MATHEMATICA
Table[Length[ContinuedFraction[Sum[1/(1 + 2^2^k), {k, 0, v}]]], {v, 0, 20}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Enrique Pérez Herrero, Apr 06 2009
EXTENSIONS
Offset corrected and a(21)-a(29) added by Amiram Eldar, May 05 2024
STATUS
approved