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A352678
Expansion of sqrt(2) in base phi where phi = (1+sqrt(5))/2.
0
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
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
KEYWORD
nonn,cons,base
AUTHOR
STATUS
approved