A394739 a(1) = 1, a(n) is the number of previous terms that are greater than half of the previous term.

1, 1, 2, 1, 4, 1, 6, 2, 4, 3, 6, 4, 6, 6, 7, 8, 6, 10, 8, 9, 10, 11, 12, 8, 14, 9, 16, 8, 18, 7, 23, 5, 26, 5, 28, 5, 30, 6, 31, 7, 33, 7, 35, 8, 34, 9, 36, 9, 38, 10, 37, 11, 39, 12, 35, 14, 33, 15, 35, 16, 32, 17, 34, 18, 32, 21, 31, 25, 29, 28, 29, 30, 30

Offset

1,3

Comments

Instead of comparing previous terms with half of the previous term, one can define a sequence that compares each term with beta times the previous term, where 0 < beta < 1. Such a sequence can potentially also produce a fractal-like structure.

Links

Nicolas Bělohoubek, Table of n, a(n) for n = 1..10000

Nicolas Bělohoubek, Scatterplot of (log_4.5(n), a(n)/n), 0 < n < 4.5^8

Nicolas Bělohoubek, Scatterplot of (log_4.5(n), a(n)/n), 4.5^7.089 < n < 4.5^7.113

Rémy Sigrist, Scatterplot of (n, k) such that a(k) > floor(a(n)/2) and 1 <= k <= n <= 1000

Formula

1 <= a(n) <= n.

Mathematica

s={1}; Do[AppendTo[s, Length[Select[s, #>s[[-1]]/2&]]], {i, 72}]; s (* James C. McMahon, May 05 2026 *)

Prog

(Python)
from itertools import islice
from collections import Counter
def agen(): # generator of terms
    c, an = Counter(), 1
    while True:
        c[an] += 1
        yield an
        t = an//2
        an = sum(c[ci] for ci in c if ci > t)
print(list(islice(agen(), 74))) # Michael S. Branicky, Apr 30 2026

Crossrefs

Sequence in context: A060794 A300716 A074919 * A362232 A138009 A131755

Adjacent sequences: A394736 A394737 A394738 * A394740 A394741 A394742

Keyword

nonn,look

Author

Nicolas Bělohoubek, Apr 29 2026

Status

approved