A355621 a(1) = 1; for n > 1, a(n) is the number of terms in the first n-1 terms of the sequence that share a 1-bit with a(n-1) in their binary expansions.

1, 1, 2, 1, 3, 5, 5, 6, 5, 8, 1, 8, 2, 4, 5, 11, 15, 17, 12, 11, 19, 17, 15, 23, 22, 19, 22, 21, 24, 16, 10, 18, 20, 21, 29, 33, 22, 30, 33, 23, 38, 31, 42, 28, 35, 37, 38, 37, 40, 22, 41, 40, 24, 33, 35, 46, 49, 49, 50, 47, 59, 60, 55, 61, 62, 61, 64, 1, 39, 63, 69, 58, 60, 64, 3, 60, 65, 46, 67

Offset

1,3

Comments

The indices where a(n) = 1 in the first 500000 terms are 1, 2, 4, 11, 68, 131, 2051, 4099. It is unknown if more exist. Many terms of the sequence are close to the line a(n) = n although only the first term is a possible fixed point. In the first 500000 terms the lowest values not to appear are 7, 9, 14, 25, 26. It is likely these and other numbers never appear although this is unknown.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Scott R. Shannon, Image of the first 500000 terms. The green line is y = n.

Example

a(7) = 5 as a(6) = 5 and the total number of terms in the first six terms that share a 1-bit with 5 in their binary expansions is five, namely 1, 1, 1, 3, 5.

Prog

(Python)
from itertools import count, islice
def agen():
    an, alst = 1, [1]
    for n in count(2):
        yield an
        an = sum(1 for k in alst if k&an)
        alst.append(an)
print(list(islice(agen(), 79))) # Michael S. Branicky, Jul 10 2022

Crossrefs

Cf. A355625, A030190, A129760, A353989, A352763, A354606.

Sequence in context: A330411 A306977 A137655 * A296064 A167595 A328600

Adjacent sequences: A355618 A355619 A355620 * A355622 A355623 A355624

Keyword

nonn,base

Author

Scott R. Shannon, Jul 10 2022

Status

approved