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Expansion of sqrt(3) in base phi where phi = (1+sqrt(5))/2.
0

%I #19 Dec 04 2022 16:31:20

%S 1,0,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,1,0,1,0,0,0,0,0,1,0,1,0,1,0,0,1,0,

%T 0,0,0,0,0,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,

%U 1,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0,0,1

%N Expansion of sqrt(3) in base phi where phi = (1+sqrt(5))/2.

%F sqrt(3) = phi + 1/phi^5 + 1/phi^8 + 1/phi^13 + 1/phi^16 + ...

%e 10.00001001000010010100000101010010000001010100001010101... base phi.

%t RealDigits[Sqrt[3],GoldenRatio,90][[1]] (* _Harvey P. Dale_, Dec 04 2022 *)

%o (PARI)

%o alist(len) = {

%o my(phi = quadgen(5), w=phi^2, t = 0);

%o vector(len, i,

%o w /= phi;

%o if ( ( t + w )^2 <= 3,

%o t += w;

%o 1,

%o 0))

%o };

%o print(alist(300));

%Y Cf. A001622, A002194, A004547.

%K nonn,cons,base

%O 2

%A _Chittaranjan Pardeshi_, Apr 29 2022