A141848 Decimal expansion of the Pell constant.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 119.

Links

Table of n, a(n) for n=0..104.

Wieb Bosma and Peter Stevenhagen, Density computations for real quadratic units, Mathematics of Computation, Vol. 65, No. 215 (1996), pp. 1327-1337.

Peter Stevenhagen, The number of real quadratic fields having units of negative norm, Experimental Mathematics, Vol. 2, No. 2 (1993), pp. 121-136; alternative link.

Peter Stevenhagen, A density conjecture for the negative Pell equation, in: W. Bosma, A. van der Poorten (eds.), Computational Algebra and Number Theory, Springer, Dordrecht, 1995, pp. 187-200.

Eric Weisstein's World of Mathematics, Pell Constant.

Formula

Equals 1 - QPochhammer(1/2, 1/4).

Equals 1 - Product_{n>=0} (1 - 1/2^(2*n+1)). - Jean-François Alcover, May 20 2014

Equals 1 - A132020. - Amiram Eldar, Apr 11 2022

Example

0.58057755820489240229...

Mathematica

RealDigits[1-QPochhammer[1/2, 1/4], 10, 120][[1]] (* Harvey P. Dale, Dec 17 2011 *)

Crossrefs

Cf. A132020.

Sequence in context: A198360 A153420 A193505 * A349398 A349397 A140249

Adjacent sequences: A141845 A141846 A141847 * A141849 A141850 A141851

Keyword

nonn,cons

Author

Eric W. Weisstein, Jul 11 2008

Status

approved