A157238 0-1 sequence generated by starting with a 0, and then by using whichever of 0, 1 will result in the shortest sequence repeated at the end.

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

Offset

1,1

Comments

The same as the Linus sequence (A006345): a(n) "breaks the pattern" by avoiding the longest doubled suffix, but using 0's and 1's. - Robert G. Wilson v, Dec 01 2013

Links

Table of n, a(n) for n=1..100.

Formula

a(n) = A006345(n) - 1. - Robert G. Wilson v, Dec 02 2013

Example

a(6)=1 as 0,1,0,0,1,1 has a longest repeated sequence of length 1 at the end, whereas 0,1,0,0,1,0 has a longest repeated sequence of length 3 at the end. Similarly, a(7)=0 since 0,1,0,0,1,1,0 has a longest repeated sequence of length 0 at the end.

Prog

(Python)
x = [0]
while len(x) < 1000:
    t = x[-1]
    z = 1
    while 2 * z + 1 <= len(x):
        if x[-z:] == x[-(2 * z + 1) : -(z + 1)]:
            t = x[-(z + 1)]
        z += 1
    x.append(1 - t)
print(x)

Crossrefs

Cf. A006345, A283131.

Sequence in context: A368463 A080846 A082401 * A337546 A059448 A283318

Adjacent sequences: A157235 A157236 A157237 * A157239 A157240 A157241

Keyword

nonn

Author

Luke Pebody (luke.pebody(AT)gmail.com), Feb 25 2009

Status

approved