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%I #12 Jun 06 2021 07:32:30
%S 2,1,1,8,0,3,3,9,8,8,7,4,9,8,9,4,8,4,8,2,0,4,5,8,6,8,3,4,3,6,5,6,3,8,
%T 1,1,7,7,2,0,3,0,9,1,7,9,8,0,5,7,6,2,8,6,2,1,3,5,4,4,8,6,2,2,7,0,5,2,
%U 6,0,4,6,2,8,1,8,9,0,2,4,4,9,7,0,7,2,0,7,2,0,4,1,8,9,3,9,1,1,3,7,4,8,4,7,5
%N Decimal expansion of (2+sqrt(5))/2.
%C Continued fraction expansion of (2+sqrt(5))/2 is A010698.
%C a(n) = A020837(n-1) for n > 1; a(1) = 2.
%F Equals 1/2 + phi, with phi = A001622.
%F From _Amiram Eldar_, Jun 06 2021: (Start)
%F Equals 1 + Sum{k>=0} 1/(Fibonacci(2*k+1)+1).
%F Equals 1 + Sum{k>=0} binomial(2*k,k)/20^k. (End)
%e 2.11803398874989484820...
%t RealDigits[GoldenRatio + 1/2, 10, 100][[1]] (* _Amiram Eldar_, Jun 06 2021 *)
%Y Cf. A002163 (sqrt(5)), A020837 (1/sqrt(80)), A010698 (repeat 2, 8).
%Y Cf. A000045, A001622.
%K cons,easy,nonn
%O 1,1
%A _Klaus Brockhaus_, Apr 07 2010
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