A355625 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 n in their binary expansions.

1, 0, 1, 0, 2, 1, 4, 0, 3, 2, 6, 2, 6, 7, 11, 0, 6, 9, 13, 6, 13, 13, 18, 6, 11, 17, 21, 16, 21, 22, 26, 0, 14, 16, 26, 14, 23, 25, 31, 12, 22, 27, 34, 27, 33, 34, 39, 19, 31, 35, 43, 36, 44, 44, 49, 36, 42, 48, 52, 47, 52, 53, 57, 0, 29, 32, 48, 30, 48, 48, 57, 25, 41, 46, 56, 47, 57, 58, 65, 34

Offset

1,5

Comments

The indices where a(n) = 1 in the first 500000 terms are 1, 3, 6. It is likely no more exist although this is unknown. 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 5, 8, 10, 15, 20, 24, 28. It is likely these and other numbers never appear although this is unknown. All terms for n > 1 where n is a power of 2 equal 0.

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) = 4 as the total number of terms in the first six terms that share a 1-bit with 7 in their binary expansions is four, namely 1, 1, 2, 1.

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&n)
        alst.append(an)
print(list(islice(agen(), 80))) # Michael S. Branicky, Jul 10 2022

Crossrefs

Cf. A355621, A030190, A129760, A353989, A352763, A354606.

Sequence in context: A158285 A277994 A334112 * A286238 A286237 A059781

Adjacent sequences: A355622 A355623 A355624 * A355626 A355627 A355628

Keyword

nonn,base

Author

Scott R. Shannon, Jul 10 2022

Status

approved