A330243 Numbers k such that the first digit of the decimal expansion of 2^k is 7.

46, 56, 66, 76, 86, 96, 149, 159, 169, 179, 189, 242, 252, 262, 272, 282, 292, 345, 355, 365, 375, 385, 438, 448, 458, 468, 478, 488, 531, 541, 551, 561, 571, 581, 634, 644, 654, 664, 674, 727, 737, 747, 757, 767, 777, 830, 840, 850, 860, 870, 923, 933, 943, 953

Offset

1,1

Comments

The asymptotic density of this sequence is log_10(8/7) = 0.057991... - Amiram Eldar, Jan 27 2021

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

70368744177664 = 2^46.

Mathematica

Select[Range[1000], Floor[2^# / 10^(Floor[# * Log10[2]])] == 7 &] (* Amiram Eldar, Dec 07 2019 *)
Select[Range[1000], IntegerDigits[2^#][[1]]==7&] (* or *) Select[Range[ 1000], NumberDigit[2^#, IntegerLength[2^#]-1]==7&] (* Harvey P. Dale, Aug 10 2021 *)

Prog

(C#)
public static void Main()
{
     for(int a = 1; a <= 10000; a++)
     {
          BigInteger n1 = BigInteger.Pow(2, a);
          string n2 = Convert.ToString(n1);
          if(n2.StartsWith("7"))
          {
          Console.WriteLine(a);
          }
     }
}
(Python)
A330243_list = [n for n in range(10**3) if str(2**n)[0] == '7'] # Chai Wah Wu, Dec 12 2019

Crossrefs

Cf. A000030, A000079, A008952, A067469, A067497, A172404.

Sequence in context: A336098 A115444 A119385 * A326646 A332952 A308099

Adjacent sequences: A330240 A330241 A330242 * A330244 A330245 A330246

Keyword

nonn,easy,base

Author

Eder Vanzei, Dec 06 2019

Status

approved