A084255 Decimal expansion of continued fraction 1/(2+1/(3+1/(5+1/(7+1/(11+...))))).

4, 3, 2, 3, 3, 2, 0, 8, 7, 1, 8, 5, 9, 0, 2, 8, 6, 8, 9, 0, 9, 2, 5, 3, 7, 9, 3, 2, 4, 1, 9, 9, 9, 9, 6, 3, 7, 0, 5, 1, 1, 0, 8, 9, 6, 8, 7, 7, 6, 5, 1, 3, 1, 0, 3, 2, 8, 1, 5, 2, 0, 6, 7, 1, 5, 8, 5, 5, 3, 9, 0, 5, 1, 1, 5, 2, 9, 5, 8, 8, 6, 6, 4, 2, 4, 7, 7, 3, 0, 2, 3, 4, 6, 7, 5, 3, 0, 7, 3, 1, 2, 9

Offset: 0

Author

Frank Ellermann, May 23 2003

Keywords

• nonn
• cons

Comments

Decimal expansion of the constant whose continued fraction form is the sequence of all the prime numbers.

Examples

			0.4323320871859028689...
		

Links

• Michael Hartley, 0.4323320871859028689.., Prime Curios!
• G. L. Honaker, Jr., Prime Curios! 0.4323320871859028689...
• Marek Wolf, Continued fractions constructed from prime numbers, arxiv:1003.4015 [math.NT], 2010.

Crossrefs

Cf. A000040, A084256, A084257, A152062

Programs

Mathematica

RealDigits[1/FromContinuedFraction@ Prime@ Range@ 34, 10, 111] (* or *)
RealDigits[ Fold[1/(#1 + #2) &, 1, Reverse@ Prime@ Range@35], 10, 111] (* Robert G. Wilson v, Dec 26 2016 *)

Formula

1/A064442. - Franklin T. Adams-Watters, Jul 31 2009