A157698 Decimal expansion of sqrt(2)*(1 + 1/sqrt(3)) + 2*sqrt(2/5 + 1/sqrt(5)).

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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

D. H. Lehmer, Interesting series involving the Central Binomial Coefficient, Am. Math. Monthly, Vol. 92, No. 7 (1985), 449-457.

Index entries for algebraic numbers, degree 16.

Formula

Equals 4*Sum_{n>=0} binomial(8*n,4*n)/8^(4*n).

Minimal polynomial: 2562890625*x^16 - 87480000000*x^14 + 1043928000000*x^12 - 5828889600000*x^10 + 15807571200000*x^8 - 18602459136000*x^6 + 9825406156800*x^4 - 4222699438080*x^2 + 472111906816. - Amiram Eldar, Jun 15 2026

Example

4.0715942738206731530648... = 4 * 1.017898568455...

Maple

sqrt(2)+sqrt(6)/3+2*sqrt(2/5+1/sqrt(5)) ;

Mathematica

RealDigits[Sqrt[2] + Sqrt[6]/3 + 2*Sqrt[2/5 + 1/Sqrt[5]], 10, 100][[1]] (* G. C. Greubel, Oct 02 2018 *)

Prog

(PARI) default(realprecision, 100); sqrt(2)+sqrt(6)/3+2*sqrt(2/5+1/sqrt(5)) \\ G. C. Greubel, Oct 02 2018
(Magma) SetDefaultRealField(RealField(100)); Sqrt(2)+Sqrt(6)/3+2*Sqrt(2/5+1/Sqrt(5)); // G. C. Greubel, Oct 02 2018

Crossrefs

Sequence in context: A354450 A199071 A351898 * A386735 A342360 A251967

Adjacent sequences: A157695 A157696 A157697 * A157699 A157700 A157701

Keyword

cons,easy,nonn

Author

R. J. Mathar, Mar 04 2009

Status

approved