A352679 Expansion of sqrt(3) in base phi where phi = (1+sqrt(5))/2.

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, 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, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1

Offset

2

Links

Table of n, a(n) for n=2..87.

Formula

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

Example

10.00001001000010010100000101010010000001010100001010101... base phi.

Mathematica

RealDigits[Sqrt[3], GoldenRatio, 90][[1]] (* Harvey P. Dale, Dec 04 2022 *)

Prog

(PARI)
alist(len) = {
    my(phi = quadgen(5), w=phi^2, t = 0);
    vector(len, i,
        w /= phi;
        if ( ( t + w )^2 <= 3,
            t += w;
            1,
            0))
};
print(alist(300));

Crossrefs

Cf. A001622, A002194, A004547.

Sequence in context: A089010 A162289 A122276 * A239199 A265718 A267463

Adjacent sequences: A352676 A352677 A352678 * A352680 A352681 A352682

Keyword

nonn,cons,base

Author

Chittaranjan Pardeshi, Apr 29 2022

Status

approved