A118502 Numbers k that divide floor((4/3)^k).

1, 7, 14, 21, 66, 205, 583, 837, 1259, 1631, 2178, 6346, 15851, 58371, 61804, 129196, 409879, 1670753, 9631198, 11292438, 17508772

Offset

1,2

Comments

Next term after 409879 is greater than 10^6.

a(22) > 10^8. - Martin Fuller, Feb 25 2026

Links

Table of n, a(n) for n=1..21.

Example

floor((4/3)^21) = 420 and 420 is divisible by 21, so 21 is in the sequence.

Mathematica

t = 1; Do[t = 4t/3; If[Mod[Floor[t], n] == 0, Print[n]], {n, 10^6}]

Prog

(Python)
from itertools import count, islice
def A118502_gen(): # generator of terms
    m, k = 1, 1
    for n in count(1):
        m <<= 2
        k *= 3
        if m//k % n == 0:
            yield n
A118502_list = list(islice(A118502_gen(), 10)) # Chai Wah Wu, Feb 08 2026
(PARI) \\ It is faster to update mixed fractions a+(b/c) than to divide 4^k/3^k each iteration.
{ my(a=1, b=0, c=1);
for(k=1, 10^6,
  my(r = divrem(a<<2, 3)); a=r[1]; r=r[2];
  b <<= 2; if(r==1, b+=c, r==2, b+=c<<1);
  c *= 3;
  if(b >= c, a++; b-=c);
  if(a % k == 0, print1(k, ", "));
); } \\ Martin Fuller, Feb 25 2026

Crossrefs

Cf. A073633.

Sequence in context: A028555 A061823 A018890 * A190367 A246172 A366112

Adjacent sequences: A118499 A118500 A118501 * A118503 A118504 A118505

Keyword

nonn,more

Author

Ryan Propper, May 06 2006

Extensions

a(18) from Ryan Propper, Jul 21 2006

a(19) from Chai Wah Wu, Feb 13 2026

a(20),a(21) from Martin Fuller, Feb 25 2026

Status

approved