A320930 Numbers k such that 4^k starts with k.

10, 17, 556, 1771, 4695, 38537, 56969, 345797, 141419115, 1788191728

Offset: 1

Author

Robert Israel, Oct 24 2018

Keywords

• nonn
• base
• more

Examples

			4^10 = 1048576 starts with 10, so 10 is in the sequence.
		

Crossrefs

Cf. A000302, A100129, A288845.

Programs

Maple

filter:= proc(n) local t, b;
  t:= 4^n;
b:= ilog10(t) - ilog10(n);
floor(t/10^b) = n
end proc:
select(filter, [$1..10^5]);

Python

def afind(limit, startk=1):
    k, pow4 = startk, 4**startk
    for k in range(startk, limit+1):
        if str(pow4).startswith(str(k)):
            print(k, end=", ")
        pow4 *= 4
afind(10**4) # Michael S. Branicky, Oct 17 2021

Extensions

a(8)-a(10) from Giovanni Resta, Oct 25 2018