A095907 Digits in the concatenation of strings formed from a previous string by substituting "01" for "0" and "011" for "1" simultaneously at each occurrence. Start with [0].

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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Chris Long, A strange recursive sequence

Formula

a(n)=1 if n = floor(phi*m) or a(n)=0 if n = floor(phi^2*m), for some positive integer m; a(0)=0 (phi denotes the golden ratio: (1 + sqrt(5))/2). a(0)=0; a(n)=1 if n belongs to A000201 (Lower Wythoff sequence) or 0 if n belongs to A001950 (Upper Wythoff sequence).

Example

0->01->01011->0101101011011->0101101011011010110101101101011011->... and then juxtapose: 0010101101011010110110101101011011010110101101101011011...

Prog

(PARI) v=[0]; for(n=1, 5, w=[]; for(k=1, length(v), if(v[k]==0, w=concat(w, [0, 1]), w=concat(w, [0, 1, 1]))); v=w; for(l=1, length(v), print1(v[l], ", ")))
(Python)
from math import isqrt
def A095907_gen(): # generator of terms
    k = 1
    for n in count(3):
        m = (n+isqrt(5*n**2)>>1)
        for _ in range(m-k-1):
            yield 0
        yield 1
        k = m
A095907_list = list(islice(A095907_gen(), 30)) # Chai Wah Wu, Aug 17 2022

Crossrefs

Cf. A005614, A096270, A114986, A189479.

Sequence in context: A327208 A178226 A288622 * A056051 A143541 A359583

Adjacent sequences: A095904 A095905 A095906 * A095908 A095909 A095910

Keyword

nonn

Author

Herman Jamke (hermanjamke(AT)fastmail.fm), Jul 13 2004

Status

approved