A362100 Numbers k such that 8^k starts with k.

4, 10, 18, 652, 1299, 8225, 12949, 56230, 156277, 3227298, 144225157

Offset: 1

Author

N. J. A. Sloane, Apr 10 2023, based on an email from Keith F. Lynch

Keywords

• nonn
• base
• more

Crossrefs

For k such that b^k starts with n, for b = 2,..., 9, see A100129, A362096, A320930, A362097-A362101.

Programs

Maple

filter:= proc(n) local d1, d2, t;
  t:= 8^n;
  d1:= ilog10(t);
  d2:= ilog10(n);
  floor(t/10^(d1-d2)) = n
end proc:
select(filter, [$1..10^5]); # Robert Israel, Apr 10 2023

Python

from itertools import count, islice
def A362100_gen(startvalue=1): # generator of terms >= startvalue
    a = 1<<3*(m:=max(startvalue,1))
    for n in count(m):
        if (s:=str(n))==str(a)[:len(s)]:
            yield n
        a <<= 3
A362100_list = list(islice(A362100_gen(),5)) # Chai Wah Wu, Apr 10 2023