

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
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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 NAS7100, 4 pp., Jet Propulsion Laboratory, Jan 01 1962.


LINKS

Table of n, a(n) for n=1..23.


FORMULA

Sum(i = 1..infinity) 1/A019434(i) = sum(i = 1..infinity) primes of form 2^(2^k) + 1, for some k >= 0. This is strictly less than sum(i = 1..infinity) 2^(2^i) + 1. It is approximated by sum(i = 1..5) 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 A113211
Adjacent sequences: A173992 A173993 A173994 * A173996 A173997 A173998


KEYWORD

cofr,nonn


AUTHOR

Jonathan Vos Post, Mar 04 2010


EXTENSIONS

Sequence corrected and comments added by Charles R Greathouse IV, Feb 04 2011


STATUS

approved



