A330243 - OEIS

%I #34 Aug 10 2021 10:54:26

%S 46,56,66,76,86,96,149,159,169,179,189,242,252,262,272,282,292,345,

%T 355,365,375,385,438,448,458,468,478,488,531,541,551,561,571,581,634,

%U 644,654,664,674,727,737,747,757,767,777,830,840,850,860,870,923,933,943,953

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

%C The asymptotic density of this sequence is log_10(8/7) = 0.057991... - _Amiram Eldar_, Jan 27 2021

%H Chai Wah Wu, <a href="/A330243/b330243.txt">Table of n, a(n) for n = 1..10000</a>

%e 70368744177664 = 2^46.

%t Select[Range[1000], Floor[2^# / 10^(Floor[# * Log10[2]])] == 7 &] (* _Amiram Eldar_, Dec 07 2019 *)

%t Select[Range[1000],IntegerDigits[2^#][[1]]==7&] (* or *) Select[Range[ 1000],NumberDigit[2^#,IntegerLength[2^#]-1]==7&] (* _Harvey P. Dale_, Aug 10 2021 *)

%o (C#)

%o public static void Main()

%o {

%o      for(int a = 1; a <= 10000; a++)

%o      {

%o           BigInteger n1 = BigInteger.Pow(2, a);

%o           string n2 = Convert.ToString(n1);

%o           if(n2.StartsWith("7"))

%o           {

%o           Console.WriteLine(a);

%o           }

%o      }

%o }

%o (Python)

%o A330243_list = [n for n in range(10**3) if str(2**n)[0] == '7'] # _Chai Wah Wu_, Dec 12 2019

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

%K nonn,easy,base

%O 1,1

%A _Eder Vanzei_, Dec 06 2019