A173995 Continued fraction expansion of sum of reciprocals of Fermat primes.

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

Author

Jonathan Vos Post, Mar 04 2010

Keywords

• cofr
• nonn
• more

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.

Examples

			(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.
		

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.

Crossrefs

Cf. A019434, A000215, A159611, A173898 (sum of reciprocals of Mersenne primes), A007400.

Programs

Mathematica

(* Assuming 65537 is the largest Fermat prime *) ContinuedFraction[Sum[1/(2^(2^n) + 1), {n, 0, 4}]] (* Alonso del Arte, Apr 21 2013 *)

Formula

Continued fraction of Sum_{i >= 1} 1/A019434(i).

Extensions

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