A188426 Position of 3^n in A051037 (5-smooth numbers).

1, 3, 8, 17, 31, 50, 77, 112, 157, 211, 276, 355, 448, 554, 676, 815, 973, 1149, 1344, 1561, 1801, 2064, 2351, 2663, 3003, 3371, 3766, 4190, 4647, 5135, 5657, 6212, 6802, 7430, 8094, 8797, 9539, 10322, 11147, 12014, 12925, 13881, 14883, 15933, 17031, 18178, 19375, 20624, 21925, 23281, 24690

Offset

0,2

Links

Zak Seidov, Table of n, a(n) for n = 0..150

Formula

A051037(a(n)) = 3^n.

a(n) ~ c * n^3, where c = log(3)^2/(6*log(2)*log(5)) = 0.180317536836709... - Vaclav Kotesovec and Amiram Eldar, Sep 22 2024

Prog

(Python)
def A188426(n):
    c, m = 0, 3**n
    i, i5 = 0, 1
    while i5<=m:
        j, j3 = 0, 1
        y = m//i5
        z = y
        while j3 <= y:
            c += z.bit_length()
            j += 1
            j3 *= 3
            z //= 3
        i += 1
        i5 *= 5
    return c # Chai Wah Wu, Mar 12 2026

Crossrefs

Cf. A051037, A188425, A188427 (powers of 2 and 5).

Sequence in context: A024929 A033816 A011889 * A349975 A105163 A011850

Adjacent sequences: A188423 A188424 A188425 * A188427 A188428 A188429

Keyword

nonn

Author

Zak Seidov, Mar 31 2011

Status

approved