A048652 Continued fraction for Product_{k >= 1} (1-1/2^k) (Cf. A048651).

0, 3, 2, 6, 4, 1, 2, 1, 9, 2, 1, 2, 3, 2, 3, 5, 1, 2, 1, 1, 6, 1, 2, 5, 79, 6, 4, 5, 1, 1, 1, 1, 12, 1, 1, 2, 5, 1, 659, 2, 17, 1, 5, 2, 3, 2, 6, 1, 1, 2, 3, 1, 2, 6, 1, 1, 3, 11, 1, 1, 2, 1, 1, 2, 4, 11, 2, 1, 3, 4, 2, 2, 1, 3, 1, 71, 1, 1, 1, 19, 1, 4, 1, 1, 8, 1, 49, 3, 1, 2, 2, 11, 1, 11, 10, 1, 2, 1, 1

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr

Comments

Continued fraction expansion of the constant Product{k>=1} (1-1/2^k)^(-1) = 3.46274661945506361... (A065446) gives essentially the same sequence.

Examples

			0.2887880950866024212788997219294585937270...
0.288788095086602421278899721... = 0 + 1/(3 + 1/(2 + 1/(6 + 1/(4 + ...)))). - _Harry J. Smith_, May 02 2009
		

References

• Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20000
• Steven R. Finch, Minkowski's Question Mark Function [Broken link]
• Steven R. Finch, Minkowski's Question Mark Function [From the Wayback machine]
• G. Xiao, Contfrac
• Index entries for continued fractions for constants

Crossrefs

Cf. A005329, A048651, A065446.

Programs

Mathematica

ContinuedFraction[ N[ Product[ 1/(1 - 1/2^k), {k, 1, Infinity} ], 500 ], 49]

PARI

{ allocatemem(932245000); default(realprecision, 21000); x=prodinf(k=1, -1/2^k, 1); z=contfrac(x); for (n=1, 20001, write("b048652.txt", n-1, " ", z[n])); } \\ Harry J. Smith, May 07 2009

Extensions

Corrected by Harry J. Smith, May 02 2009

Deleted old PARI program. - Harry J. Smith, May 20 2009