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URL: https://oeis.org/A108238

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A108238
Numbers of the form (7^i)*(12^j), with i, j >= 0.
3
1, 7, 12, 49, 84, 144, 343, 588, 1008, 1728, 2401, 4116, 7056, 12096, 16807, 20736, 28812, 49392, 84672, 117649, 145152, 201684, 248832, 345744, 592704, 823543, 1016064, 1411788, 1741824, 2420208, 2985984, 4148928, 5764801, 7112448
OFFSET
1,2
LINKS
FORMULA
Sum_{n>=1} 1/a(n) = (7*12)/((7-1)*(12-1)) = 14/11. - Amiram Eldar, Sep 26 2020
a(n) ~ exp(sqrt(2*log(7)*log(12)*n)) / sqrt(84). - Vaclav Kotesovec, Sep 26 2020
MATHEMATICA
Take[7^#[[1]]*12^#[[2]]&/@Tuples[Range[0, 10], 2]//Union, 40] (* Harvey P. Dale, Mar 05 2017 *)
n = 10^6; Flatten[Table[7^i*12^j, {i, 0, Log[7, n]}, {j, 0, Log[12, n/7^i]}]] // Sort (* Amiram Eldar, Sep 26 2020 *)
PROG
(Python)
from sympy import integer_log
def A108238(n):
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
kmin = kmax >> 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
def f(x): return n+x-sum(integer_log(x//12**i, 7)[0]+1 for i in range(integer_log(x, 12)[0]+1))
return bisection(f, n, n) # Chai Wah Wu, Mar 26 2025
KEYWORD
nonn,easy
AUTHOR
Douglas Winston (douglas.winston(AT)srupc.com), Jun 17 2005
STATUS
approved