cp's OEIS Frontend

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

%I A330243 #34 Aug 10 2021 10:54:26
%S A330243 46,56,66,76,86,96,149,159,169,179,189,242,252,262,272,282,292,345,
%T A330243 355,365,375,385,438,448,458,468,478,488,531,541,551,561,571,581,634,
%U A330243 644,654,664,674,727,737,747,757,767,777,830,840,850,860,870,923,933,943,953
%N A330243 Numbers k such that the first digit of the decimal expansion of 2^k is 7.
%C A330243 The asymptotic density of this sequence is log_10(8/7) = 0.057991... - _Amiram Eldar_, Jan 27 2021
%H A330243 Chai Wah Wu, <a href="/A330243/b330243.txt">Table of n, a(n) for n = 1..10000</a>
%e A330243 70368744177664 = 2^46.
%t A330243 Select[Range[1000], Floor[2^# / 10^(Floor[# * Log10[2]])] == 7 &] (* _Amiram Eldar_, Dec 07 2019 *)
%t A330243 Select[Range[1000],IntegerDigits[2^#][[1]]==7&] (* or *) Select[Range[ 1000],NumberDigit[2^#,IntegerLength[2^#]-1]==7&] (* _Harvey P. Dale_, Aug 10 2021 *)
%o A330243 (C#)
%o A330243 public static void Main()
%o A330243 {
%o A330243      for(int a = 1; a <= 10000; a++)
%o A330243      {
%o A330243           BigInteger n1 = BigInteger.Pow(2, a);
%o A330243           string n2 = Convert.ToString(n1);
%o A330243           if(n2.StartsWith("7"))
%o A330243           {
%o A330243           Console.WriteLine(a);
%o A330243           }
%o A330243      }
%o A330243 }
%o A330243 (Python)
%o A330243 A330243_list = [n for n in range(10**3) if str(2**n)[0] == '7'] # _Chai Wah Wu_, Dec 12 2019
%Y A330243 Cf. A000030, A000079, A008952, A067469, A067497, A172404.
%K A330243 nonn,easy,base
%O A330243 1,1
%A A330243 _Eder Vanzei_, Dec 06 2019