cp's OEIS Frontend

A141848 Decimal expansion of the Pell constant.

%I A141848 #24 Feb 16 2025 08:33:08
%S A141848 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,
%T A141848 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,
%U A141848 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
%N A141848 Decimal expansion of the Pell constant.
%D A141848 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.8, pp. 119-120.
%H A141848 Wieb Bosma and Peter Stevenhagen, <a href="https://doi.org/10.1090/S0025-5718-96-00725-9">Density computations for real quadratic units</a>, Mathematics of Computation, Vol. 65, No. 215 (1996), pp. 1327-1337.
%H A141848 Peter Stevenhagen, <a href="https://doi.org/10.1080/10586458.1993.10504272">The number of real quadratic fields having units of negative norm</a>, Experimental Mathematics, Vol. 2, No. 2 (1993), pp. 121-136; <a href="https://projecteuclid.org/journals/experimental-mathematics/volume-2/issue-2/The-number-of-real-quadratic-fields-having-units-of-negative/em/1048516217.full">alternative link</a>.
%H A141848 Peter Stevenhagen, <a href="https://doi.org/10.1007/978-94-017-1108-1_13">A density conjecture for the negative Pell equation</a>, in: W. Bosma, A. van der Poorten (eds.), Computational Algebra and Number Theory, Springer, Dordrecht, 1995, pp. 187-200.
%H A141848 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PellConstant.html">Pell Constant</a>.
%F A141848 Equals 1 - QPochhammer(1/2, 1/4).
%F A141848 Equals 1 - Product_{n>=0} (1 - 1/2^(2*n+1)). - _Jean-François Alcover_, May 20 2014
%F A141848 Equals 1 - A132020. - _Amiram Eldar_, Apr 11 2022
%e A141848 0.58057755820489240229...
%t A141848 RealDigits[1-QPochhammer[1/2,1/4],10,120][[1]] (* _Harvey P. Dale_, Dec 17 2011 *)
%Y A141848 Cf. A132020.
%K A141848 nonn,cons
%O A141848 0,1
%A A141848 _Eric W. Weisstein_, Jul 11 2008