A320930 - OEIS

%I #15 Oct 20 2021 08:02:55

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

%N Numbers k such that 4^k starts with k.

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

%p filter:= proc(n) local t, b;

%p   t:= 4^n;

%p b:= ilog10(t) - ilog10(n);

%p floor(t/10^b) = n

%p end proc:

%p select(filter, [$1..10^5]);

%o (Python)

%o def afind(limit, startk=1):

%o     k, pow4 = startk, 4**startk

%o     for k in range(startk, limit+1):

%o         if str(pow4).startswith(str(k)):

%o             print(k, end=", ")

%o         pow4 *= 4

%o afind(10**4) # _Michael S. Branicky_, Oct 17 2021

%Y Cf. A000302, A100129, A288845.

%K nonn,base,more

%O 1,1

%A _Robert Israel_, Oct 24 2018

%E a(8)-a(10) from _Giovanni Resta_, Oct 25 2018