A352715 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 floor(k/2) common 1-bits in their binary representations, where k is the number of bits in the binary representation of a(n-1).

1, 2, 3, 5, 4, 6, 10, 11, 7, 9, 13, 12, 14, 22, 15, 19, 17, 21, 20, 23, 18, 26, 24, 25, 28, 27, 35, 39, 31, 37, 45, 29, 41, 43, 42, 46, 30, 38, 47, 44, 60, 52, 53, 49, 51, 50, 54, 58, 55, 57, 56, 59, 75, 63, 71, 67, 79, 61, 77, 69, 85, 81, 83, 82, 86, 62, 78, 70

Offset

1,2

Comments

A variant of A109812. Sharing floor(k/2) common 1-bits is akin to minimal or zero correlation between sequences whose elements are in {+1,-1}.

Links

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

Rémy Sigrist, PARI program

Prog

(PARI) See Links section.
(Python 3.10+)
from itertools import islice
def A352715_gen(): # generator of terms
    yield 1
    l1, s, b, bli = 1, 2, set(), 0
    while True:
        i = s
        while True:
            if not (i in b or (i & l1).bit_count() != bli):
                yield i
                l1 = i
                bli = l1.bit_length()//2
                b.add(i)
                while s in b:
                    b.remove(s)
                    s += 1
                break
            i += 1
A352715_list = list(islice(A352715_gen(), 20)) # Chai Wah Wu, Apr 02 2022

Crossrefs

Cf. A109812.

Sequence in context: A365390 A359557 A114744 * A096114 A344169 A121664

Adjacent sequences: A352712 A352713 A352714 * A352716 A352717 A352718

Keyword

nonn

Author

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

Status

approved