|
%I #27 Apr 29 2022 03:50:27
%S 1,0,1,1,1,1,0,1,1,1,1,1,1,0,1,0,1,1,1,1,1,1,1,1,1,0,1,0,1,1,1,1,1,1,
%T 0,1,0,1,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,
%U 0,1,1,0,1,0,1,1,0,1,1,1,0,1,1,0,1,0,1,1,0,1,1,1,0,1,1,1,1,0,1,1
%N Lazy expansion of Pi in golden base (i.e., phi = (1+sqrt(5))/2) without consecutive zeros.
%F Pi = phi^1 + phi^-1 + phi^-2 + phi^-3 + phi^-4 + phi^-6 + ...
%e 10.111101111110101...
%o (PARI)
%o f(len) = {
%o my(o=0,a=1, b=1, phi = quadgen(5), t=3, s=3, n=1, na=0, d=0, da=24);
%o vector(len, x,
%o until (b-a + a * phi < s,
%o n += na;
%o na += 8;
%o d += da;
%o da += 32;
%o t = (t*n)/d;
%o s += t;
%o );
%o if (a + b * phi <= s,
%o s -= b - a + a * phi;
%o o=1,
%o o=0
%o );
%o a = b - a;
%o b -= a;
%o o
%o )
%o };
%o print(f(200)); \\ _Chittaranjan Pardeshi_, Apr 21 2022
%Y Cf. A000796, A001622, A102243.
%K nonn,base
%O 2
%A _Chittaranjan Pardeshi_, Aug 05 2016
|
