A157698 - OEIS

%I #16 Jun 15 2026 00:43:29

%S 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,

%T 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,

%U 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

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

%H D. H. Lehmer, <a href="https://www.jstor.org/stable/2322496">Interesting series involving the Central Binomial Coefficient</a>, Am. Math. Monthly, Vol. 92, No. 7 (1985), 449-457.

%H <a href="/index/Al#algebraic_16">Index entries for algebraic numbers, degree 16</a>.

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

%F 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

%e 4.0715942738206731530648... = 4 * 1.017898568455...

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

%t RealDigits[Sqrt[2] + Sqrt[6]/3 + 2*Sqrt[2/5 + 1/Sqrt[5]], 10, 100][[1]] (* _G. C. Greubel_, Oct 02 2018 *)

%o (PARI) default(realprecision, 100); sqrt(2)+sqrt(6)/3+2*sqrt(2/5+1/sqrt(5)) \\ _G. C. Greubel_, Oct 02 2018

%o (Magma) SetDefaultRealField(RealField(100)); Sqrt(2)+Sqrt(6)/3+2*Sqrt(2/5+1/Sqrt(5)); // _G. C. Greubel_, Oct 02 2018

%K cons,easy,nonn

%O 1,1

%A _R. J. Mathar_, Mar 04 2009