A352678 Expansion of sqrt(2) in base phi where phi = (1+sqrt(5))/2.

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

Offset

1

Links

Table of n, a(n) for n=1..87.

Formula

sqrt(2) = 1 + 1/phi^2 + 1/phi^8 + 1/phi^10 + 1/phi^13 + 1/phi^15 + ...

Example

1.01000001010010100100000001010000000001010101010101001... base phi.

Mathematica

RealDigits[Sqrt[2], GoldenRatio, 100][[1]] (* Amiram Eldar, May 06 2022 *)

Prog

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

Crossrefs

Cf. A001622, A002193, A004539.

Sequence in context: A236677 A190236 A190224 * A373371 A321692 A355943

Adjacent sequences: A352675 A352676 A352677 * A352679 A352680 A352681

Keyword

nonn,cons,base

Author

Chittaranjan Pardeshi, Apr 29 2022

Status

approved