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%I #21 May 06 2022 20:04:01
%S 1,0,1,0,0,0,0,0,1,0,1,0,0,1,0,1,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,
%T 0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,0,1,0,
%U 0,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1
%N Expansion of sqrt(2) in base phi where phi = (1+sqrt(5))/2.
%F sqrt(2) = 1 + 1/phi^2 + 1/phi^8 + 1/phi^10 + 1/phi^13 + 1/phi^15 + ...
%e 1.01000001010010100100000001010000000001010101010101001... base phi.
%t RealDigits[Sqrt[2], GoldenRatio, 100][[1]] (* _Amiram Eldar_, May 06 2022 *)
%o (PARI)
%o alist(len) = {
%o my(phi = quadgen(5), w=phi, t = 0);
%o vector(len, i, w /= phi; if ( ( t + w )^2 <= 2, t += w ; 1, 0))
%o };
%o print(alist(300));
%Y Cf. A001622, A002193, A004539.
%K nonn,cons,base
%O 1
%A _Chittaranjan Pardeshi_, Apr 29 2022
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