A276690 Binary Barker codes written in base 10.

2, 3, 6, 13, 14, 29, 114, 1810, 7989

Offset

1,1

Comments

This is almost certainly the complete list of Barker codes.

Codes of the same length which also have similar autocorrelation function are considered as the same and only one code which has greatest value is stored. For example: for codes of length 5 in binary representation: 00010, 01000, 10111 and 11101 only one code 11101 (29 in decimal) should be stored. - Sergiy Piyatakov, Jan 13 2017

Links

Table of n, a(n) for n=1..9.

Eric Weisstein's World of Mathematics, Barker Code

Example

29 (binary: 11101) is in the sequence because + + + - + is a Barker code.

Prog

(Python)
def ok(n):
    t = [(-1)**int(x) for x in bin(n)[2:]]
    return all(abs(sum(t[i]*t[i+k] for i in range(len(t)-k))) <= 1 for k in range(1, len(t)))
def not_dup(n):
    b = bin(n)[2:]
    i = ''.join('0' if c=='1' else '1' for c in b)
    return b >= b[::-1] and b >= i[::-1]
a = [n for n in range(2, 2**13) if not_dup(n) and ok(n)]
print(a)
# Andrey Zabolotskiy, Jan 13 2017

Crossrefs

Cf. A091704.

Sequence in context: A187013 A295324 A054049 * A175281 A364606 A244790

Adjacent sequences: A276687 A276688 A276689 * A276691 A276692 A276693

Keyword

nonn

Author

Gordon Hamilton, Sep 13 2016

Extensions

Corrected by Sergiy Piyatakov, Jan 13 2017

Status

approved