cp's OEIS Frontend

A223140 Decimal expansion of (sqrt(29) + 1)/2.

%I A223140 #19 Feb 10 2025 12:03:51
%S A223140 3,1,9,2,5,8,2,4,0,3,5,6,7,2,5,2,0,1,5,6,2,5,3,5,5,2,4,5,7,7,0,1,6,4,
%T A223140 7,7,8,1,4,7,5,6,0,0,8,0,8,2,2,3,9,4,4,1,8,8,4,0,1,9,4,3,3,5,0,0,8,3,
%U A223140 2,2,9,8,1,4,1,3,8,2,9,3,4,6,4,3,8,3,1,6,8,9,0,8,3,9,9,1,7,7,4,2,2,0
%N A223140 Decimal expansion of (sqrt(29) + 1)/2.
%C A223140 Decimal expansion of sqrt(7 + sqrt(7 + sqrt(7 + sqrt(7 + ... )))).
%C A223140 Sequence with a(1) = 2 is decimal expansion of sqrt(7 - sqrt(7 - sqrt(7 - sqrt(7 - ... )))) - A223141.
%C A223140 From _Wolfdieter Lang_, Jan 05 2024: (Start)
%C A223140 This number phi29 = (1 + sqrt(29))/2 is the fundamental algebraic integer in the quadratic number field Q(sqrt(29)) with minimal polynomial x^2 - x - 7. The other root is -A223141.
%C A223140 phi29^n = 7*A(n-1) + A(n)*phi29, where A(n) = A015442(n) with A(-1) = 1/7, for n >= 0. For negative powers n see A367454 = 1/phi29. (End)
%H A223140 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.
%F A223140 Closed form: (sqrt(29) + 1)/2 = A098318-2 = 10*A085551+3 = A223141+1.
%F A223140 sqrt(7 + sqrt(7 + sqrt(7 + sqrt(7 + ... )))) - 1 = sqrt(7 - sqrt(7 - sqrt(7 - sqrt(7 - ... )))). See A223141.
%e A223140 3.1925824035672520156253552457701...
%t A223140 RealDigits[(1 + Sqrt[29])/2, 10, 130]
%o A223140 (PARI) (sqrt(29)+1)/2 \\ _Charles R Greathouse IV_, Feb 10 2025
%Y A223140 Cf. A223141, A367454.
%Y A223140 Essentially the same as A098318 and A085551.
%K A223140 nonn,cons
%O A223140 1,1
%A A223140 _Jaroslav Krizek_, Apr 02 2013