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

10, 17, 556, 1771, 4695, 38537, 56969, 345797, 141419115, 1788191728, 18205902108, 371894584104, 2466150711429, 160624573139585, 503605572013283, 10459364533794480, 13156513707230485

Offset

1,1

Links

Table of n, a(n) for n=1..17.

Example

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

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]);

Prog

(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

Crossrefs

b^k starts with k: A131493 (b=pi), A131494 (b=e), A100129 (b=2), A362096 (b=3), A320930 (b=4), A362097 (b=5), A362098 (b=6), A362099 (b=7), A362100 (b=8), A362101 (b=9).

Cf. A000302, A033147, A131495, A288845.

Sequence in context: A177185 A241281 A002744 * A337325 A156382 A214894

Adjacent sequences: A320927 A320928 A320929 * A320931 A320932 A320933

Keyword

nonn,base

Author

Robert Israel, Oct 24 2018

Extensions

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

a(11)-a(17) from Max Alekseyev, Nov 08 2025

Status

approved