A389763 First differences of 2-dense numbers.

1, 2, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 6, 6, 2, 4, 4, 2, 6, 8, 4, 4, 2, 6, 4, 4, 4, 4, 8, 6, 2, 4, 8, 4, 6, 6, 4, 2, 6, 8, 4, 12, 4, 2, 2, 4, 4, 2, 6, 4, 4, 4, 6, 6, 12, 4, 4, 4, 6, 2, 4, 4, 8, 6, 6, 4, 2, 2, 4, 8, 4, 6, 6, 4, 2, 10, 8, 4, 4, 10, 2, 4, 6, 2, 4, 4, 8, 6, 2, 4, 12, 8, 8, 2, 6, 4, 2, 2, 4, 8, 4

Offset

1,2

Comments

First differences of A174973.

Also distances between the 1's of A237271.

First differs from A179651 at a(23).

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

a(n) = A174973(n+1) - A174973(n).

Mathematica

Differences[Select[Range[500], Length[Split[Divisors[#], #2 <= 2*# &]] == 1 &]] (* Paolo Xausa, Oct 23 2025 *)

Prog

(Python)
from itertools import count, islice
from sympy import divisors
def A389763_gen(): # generator of terms
    m = 1
    for k in count(2):
        ds = divisors(k)
        for i in range(len(ds)-1):
            if (ds[i]<<1)<ds[i+1]:
                break
        else:
            yield k-m
            m = k
A389763_list = list(islice(A389763_gen(), 104)) # Chai Wah Wu, Oct 22 2025

Crossrefs

Cf. A005153, A174973 (2-dense numbers), A179651, A237271.

Sequence in context: A064135 A332476 A179651 * A139560 A192095 A363710

Adjacent sequences: A389760 A389761 A389762 * A389764 A389765 A389766

Keyword

nonn

Author

Omar E. Pol, Oct 20 2025

Status

approved