A372400 Position of 30^n among 5-smooth numbers A051037.

1, 18, 83, 228, 486, 888, 1466, 2255, 3283, 4583, 6189, 8134, 10445, 13158, 16305, 19916, 24027, 28667, 33870, 39665, 46086, 53166, 60937, 69429, 78675, 88709, 99561, 111263, 123849, 137347, 151793, 167219, 183658, 201139, 219695, 239359, 260165, 282141, 305320

Offset

0,2

Comments

Also position of 30^(n+1) in A143207.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..1000

Formula

a(n) = k*n^3 + (3k/2)*n^2 + O(n) where k = (log 30)^3/(6 log 2 log 3 log 5) = 5.35057081984.... - Charles R Greathouse IV, Sep 19 2024

Mathematica

Table[Sum[Floor@ Log[5, 30^n/(2^i*3^j)] + 1, {i, 0, Log[2, 30^n]}, {j, 0, Log[3, 30^n/2^i]}], {n, 0, 38}]

Prog

(Python) # uses imports/function in A372401
print(list(islice(A372401gen(p=5), 40))) # Michael S. Branicky, Jun 05 2024
(Python)
from sympy import integer_log
def A372400(n):
    c, x = 0, 30**n
    for i in range(integer_log(x, 5)[0]+1):
        for j in range(integer_log(y:=x//5**i, 3)[0]+1):
            c += (y//3**j).bit_length()
    return c # Chai Wah Wu, Sep 16 2024
(PARI) a(n)=my(t=30^n, u=5*t); sum(a=0, logint(t, 5), u\=5; sum(b=0, logint(u, 3), logint(u\3^b, 2)+1)) \\ Charles R Greathouse IV, Sep 18 2024

Crossrefs

Cf. A002110, A051037, A143207, A202821, A372401, A372402.

Sequence in context: A039358 A043961 A067984 * A281372 A124935 A126405

Adjacent sequences: A372397 A372398 A372399 * A372401 A372402 A372403

Keyword

nonn

Author

Michael De Vlieger, Jun 03 2024

Status

approved