A348446 a(n) = A307720(2*n-1) - A307220(2*n).

0, 1, 2, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 4, 4, 4, 6, 6, 6, 5, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 4, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 1, 1, 1, 1, 1, 1, 1

Offset

1,3

Comments

My guess is that this changes signs infinitely often, but is more likely to be positive than negative. Perhaps the behavior is akin to that of A066520, which shows the "great prime race" between primes congruent to 3 mod 4 and primes congruent to 1 mod 4.

See also the graphs in A307720 and A348248.

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..20000

Rémy Sigrist, Scatterplot of the first million terms

Rémy Sigrist, Scatterplot of the first five million terms

N. J. A. Sloane, Table of n, a(n) for n = 1..500000

Chai Wah Wu, Scatterplot of the first 100 million terms

Prog

(Python)
from itertools import islice
from collections import Counter
def A348446(): # generator of terms. Greedy algorithm
    a = 1
    c, b = Counter(), 1
    while True:
        k, kb = 1, b
        while c[kb] >= kb:
            k += 1
            kb += b
        c[kb] += 1
        b = k
        a2 = k
        yield a-a2
        k, kb = 1, b
        while c[kb] >= kb:
            k += 1
            kb += b
        c[kb] += 1
        b = k
        a = k
A348446_list = list(islice(A348446(), 100)) # Chai Wah Wu, Oct 23 2021

Crossrefs

Cf. A066520, A307720, A307730, A348248.

Sequence in context: A214625 A363339 A334195 * A279278 A015964 A088950

Adjacent sequences: A348443 A348444 A348445 * A348447 A348448 A348449

Keyword

sign

Author

N. J. A. Sloane, Oct 22 2021

Status

approved