login
A141848
Decimal expansion of the Pell constant.
3
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
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
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Jul 11 2008
STATUS
approved