A275694 Lazy expansion of Pi in golden base (i.e., phi = (1+sqrt(5))/2) without consecutive zeros.

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, 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, 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

Offset

2

Links

Table of n, a(n) for n=2..101.

Formula

Pi = phi^1 + phi^-1 + phi^-2 + phi^-3 + phi^-4 + phi^-6 + ...

Example

10.111101111110101...

Prog

(PARI)
f(len) = {
    my(o=0, a=1, b=1, phi = quadgen(5), t=3, s=3, n=1, na=0, d=0, da=24);
    vector(len, x,
        until (b-a + a * phi < s,
            n += na;
            na += 8;
            d += da;
            da += 32;
            t = (t*n)/d;
            s += t;
        );
        if (a + b * phi <= s,
            s -= b - a + a * phi;
            o=1,
            o=0
        );
        a = b - a;
        b -= a;
        o
    )
};
print(f(200)); \\ Chittaranjan Pardeshi, Apr 21 2022

Crossrefs

Cf. A000796, A001622, A102243.

Sequence in context: A287725 A176702 A188038 * A267922 A267358 A368281

Adjacent sequences: A275691 A275692 A275693 * A275695 A275696 A275697

Keyword

nonn,base

Author

Chittaranjan Pardeshi, Aug 05 2016

Status

approved