A094884 - OEIS

%I #24 Nov 23 2024 05:48:22

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

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

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

%N Decimal expansion of phi/sqrt(2), where phi = (1+sqrt(5))/2.

%C An algebraic number with minimal polynomial 4*x^4 - 6*x^2 + 1. - _Charles R Greathouse IV_, Mar 25 2014

%H Ivan Panchenko, <a href="/A094884/b094884.txt">Table of n, a(n) for n = 1..1000</a>

%F Equals Product_{k>=0} (1 + (-1)^k/(10*k+5)). - _Amiram Eldar_, Nov 23 2024

%F Equals A094887/2 = sqrt(A239798). - _Hugo Pfoertner_, Nov 23 2024

%e 1.144122805635368595200145567160604153072306753675541225...

%t RealDigits[GoldenRatio/Sqrt[2],10,120][[1]] (* _Harvey P. Dale_, Feb 11 2015 *)

%o (PARI) sqrt(sqrt(5)+3)/2 \\ _Charles R Greathouse IV_, Mar 25 2014

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (1+Sqrt(5) )/(2*Sqrt(2)); // _G. C. Greubel_, Sep 27 2018

%Y Cf. A001622 (phi), A002193 (sqrt(2)), A017329, A094887, A239798.

%K cons,nonn

%O 1,3

%A _N. J. A. Sloane_, Jun 15 2004