A367454 - OEIS

%I #8 Feb 14 2024 14:14:02

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

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

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

%N Decimal expansion of (-1 + sqrt(29))/14 = 1/A223140.

%C c^n = 7*A(-(n+1)) + A(-n)*phi29, for n >= 0, where phi29 = A223140, and A(-n) = A015442(-n) = sqrt(-7)^(-(n+1))*S(-(n+1), 1/sqrt(-7)) = -(i/sqrt(7))^(n+1)*S(n-1, i/sqrt(7)), with i = sqrt(-1) and the S-Chebyshev polynomials (see A049310), where S(-n, x) = -S(n-2, x), for n >= 1, and S(n, -x) = (-1)^n*S(n, x).

%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials</a>.

%F c = 1/phi29 = (-1 + phi(29))/7, with phi29 = A223140.

%e c = 0.3132260576524645736607650351100235397353657258317706312628...

%t Flatten[First[RealDigits[(-1 + Sqrt[29])/14,10,96]]] (* _Stefano Spezia_, Jan 05 2024 *)

%Y Cf. A010484, A015442, A049310, A223140.

%K nonn,cons,easy

%O 0,1

%A _Wolfdieter Lang_, Jan 05 2024