OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Sum_{n>=1} 1/a(n) = (7*13)/((7-1)*(13-1)) = 91/72. - Amiram Eldar, Sep 23 2020
a(n) ~ exp(sqrt(2*log(7)*log(13)*n)) / sqrt(91). - Vaclav Kotesovec, Sep 23 2020
MATHEMATICA
n = 10^7; Flatten[Table[7^i*13^j, {i, 0, Log[7, n]}, {j, 0, Log[13, n/7^i]}]] // Sort (* Amiram Eldar, Sep 23 2020 *)
PROG
(PARI) list(lim)=my(v=List(), N); for(n=0, log(lim)\log(13), N=13^n; while(N<=lim, listput(v, N); N*=7)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jun 28 2011
(Python)
from sympy import integer_log
def A108056(n):
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: 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//13**i, 7)[0]+1 for i in range(integer_log(x, 13)[0]+1))
return bisection(f, n, n) # Chai Wah Wu, Oct 22 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Douglas Winston (douglas.winston(AT)srupc.com), Jun 02 2005
EXTENSIONS
More terms from Amiram Eldar, Sep 23 2020
STATUS
approved