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

Author

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

Keywords

• nonn

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

Examples

			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.
		

Crossrefs

Cf. A006345, A283131.

Programs

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)

Formula

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