A159643 - OEIS

%I #16 May 07 2026 00:46:35

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

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

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

%N Decimal expansion of (1084467 + 707402*sqrt(2))/647^2.

%H G. C. Greubel, <a href="/A159643/b159643.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.

%F Equals (1226 + 577*sqrt(2))/(1226 - 577*sqrt(2)).

%F Equals (3 + 2*sqrt(2))*(36 - sqrt(2))^2/(36 + sqrt(2))^2.

%F Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 0, b = A130013.

%F Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 1, b = A159641.

%F Minimal polynomial: 418609*x^2 - 2168934*x + 418609. - _Amiram Eldar_, May 07 2026

%e 4.98050568059896510517550317093848636836843695187013...

%t RealDigits[(1084467+707402*Sqrt[2])/647^2, 10, 100][[1]] (* _G. C. Greubel_, May 10 2018 *)

%o (PARI) (1084467+707402*sqrt(2))/647^2 \\ _G. C. Greubel_, May 10 2018

%o (Magma) (1084467+707402*Sqrt(2))/647^2; // _G. C. Greubel_, May 10 2018

%Y Cf. A130013, A159641, A002193 (decimal expansion of sqrt(2)), A159642 (decimal expansion of (649+36*sqrt(2))/647).

%K cons,nonn

%O 1,1

%A _Klaus Brockhaus_, Apr 21 2009