A175924 - OEIS

%I #15 May 19 2021 15:01:05

%S 1,65536,16777216,2199023255552,

%T 1684996666696914987166688442938726917102321526408785780068975640576

%N Smallest power of 2 with n repeated digits.

%C The subsequent terms are too large to display.

%C a(6) and a(7), 2^971 and 2^972, respectively, both of which have 293 digits; a(8), 2^8554, has 2576 digits. a(9), 2^42485, has 12790 digits.

%C Corresponding exponents of 2 are 0, 16, 24, 41, 220, 971, 972, 8554, 42485, 42486, 271979. [_Zak Seidov_, Oct 19 2010]

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Power_of_2">Power of 2</a>

%e a(1) is 1 because it is the first power of 2; all integers have at least one digit.

%e a(2) is 65536 because it is the first power of 2 with two of the same digit in a row.

%e a(3) is 16777216 because it is the first power of 2 with three of the same digit in a row.

%t f[n_] := Block[{k = 0}, While[ !MemberQ[Length /@ Split@ IntegerDigits[2^k], n], k++ ]; 2^k]; Table[f[n], {n, 5}] (* _Robert G. Wilson v_, Oct 21 2010 *)

%o (Python)

%o import math

%o for N in range(1, 10):

%o     repdigits = 1

%o     n = 0

%o     while repdigits < N:

%o         n += 1

%o         s = str(2 ** n)

%o         prev = ""

%o         repdigits = maxrepdigits = 1

%o         for d in s:

%o             if d == prev: repdigits += 1

%o             else:

%o                 maxrepdigits = max(maxrepdigits, repdigits)

%o                 repdigits = 1

%o             prev = d

%o         repdigits = max(maxrepdigits, repdigits)

%o     print(N, 2 ** n)

%Y Subsequence of A000079 (powers of 2).

%Y Cf. A045875.

%K base,nonn

%O 1,2

%A _Grant Garcia_, Oct 18 2010, Oct 20 2010