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