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A173995
Continued fraction expansion of sum of reciprocals of Fermat primes.
0
0, 1, 1, 2, 9, 1, 3, 5, 1, 2, 1, 1, 1, 1, 3, 1, 7, 1, 31, 1, 2, 4, 5
OFFSET
1,4
COMMENTS
If there are only five Fermat primes, a(24) = 2 is the last term of this sequence. Otherwise, a(24) = a(25) = 1 and a(26) is large (billions of digits).
This sequence is finite if and only if A019434 is finite.
REFERENCES
S. W. Golomb, Irrationality of the sum of reciprocals of fermat numbers and other functions, NASA Technical Report 19630013175, Accession ID 63N23055, Contract/grant NAS7-100, 4 pp., Jet Propulsion Laboratory, Jan 01 1962.
FORMULA
Continued fraction of Sum_{i >= 1} 1/A019434(i).
EXAMPLE
(1/3) + (1/5) + (1/17) + (1/257) + (1/65537) = 2560071829/4294967295 = 0 + 1/1+ 1/1+ 1/2+ 1/9+ 1/1+ 1/3+ 1/5+ 1/1+ 1/2+ 1/1+ 1/1+ 1/1+ 1/1+ 1/3+ 1/1+ 1/7+ 1/1+ 1/31+ 1/1+ 1/2+ 1/4+ 1/5+ 1/2.
MATHEMATICA
(* Assuming 65537 is the largest Fermat prime *) ContinuedFraction[Sum[1/(2^(2^n) + 1), {n, 0, 4}]] (* Alonso del Arte, Apr 21 2013 *)
CROSSREFS
Cf. A019434, A000215, A159611, A173898 (sum of reciprocals of Mersenne primes), A007400.
Sequence in context: A176124 A190411 A190142 * A272868 A074950 A346170
KEYWORD
cofr,nonn,more
AUTHOR
Jonathan Vos Post, Mar 04 2010
EXTENSIONS
Sequence corrected and comments added by Charles R Greathouse IV, Feb 04 2011
STATUS
approved