A352716 a(1)=1; thereafter a(n) = smallest positive integer not among the earlier terms of the sequence such that a(n) and a(n-1) have an even number of common 1-bits in their binary representations

1, 2, 4, 3, 7, 5, 8, 6, 9, 11, 10, 14, 12, 13, 16, 15, 19, 17, 21, 20, 22, 18, 23, 25, 24, 26, 28, 27, 31, 29, 32, 30, 33, 35, 34, 38, 36, 37, 41, 39, 42, 40, 43, 44, 52, 45, 47, 46, 50, 48, 49, 54, 55, 51, 56, 53, 58, 59, 57, 61, 60, 62, 64, 63, 67, 65, 69, 68, 70, 66, 71, 73, 72, 74, 76, 75, 79, 77, 81, 80, 82, 78, 83, 84, 88, 85, 87, 86, 89, 91, 90, 94, 92

Offset

1,2

Comments

A variant of A109812. Sharing an even number of common 1-bits is equivalent to zero correlation between sequences in the vector space F_2^k.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program

Prog

(PARI) \\ See Links section.
(Python)
from itertools import islice
def A352716_gen(): # generator of terms
    yield 1
    l1, s, b = 1, 2, set()
    while True:
        i = s
        while True:
            if not (i in b or (i & l1).bit_count() % 2):
                yield i
                l1 = i
                b.add(i)
                while s in b:
                    b.remove(s)
                    s += 1
                break
            i += 1
A352716_list = list(islice(A352716_gen(), 20)) # Chai Wah Wu, Apr 02 2022

Crossrefs

Cf. A109812, A352715.

Sequence in context: A376133 A191666 A215673 * A120619 A346298 A084385

Adjacent sequences: A352713 A352714 A352715 * A352717 A352718 A352719

Keyword

nonn

Author

Chai Wah Wu, Michael De Vlieger, Rémy Sigrist, and N. J. A. Sloane, Mar 30 2022

Status

approved