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A372400
Position of 30^n among 5-smooth numbers A051037.
3
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
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Jun 03 2024
STATUS
approved