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Powers of 2 with exactly one odd decimal digit.
0

%I #30 Sep 04 2024 20:04:36

%S 1,16,32,128,256,1024,4096,262144,524288,8388608

%N Powers of 2 with exactly one odd decimal digit.

%C Inspired by A068994 (Powers of 2 such that number of odd digits is 0).

%C No additional terms up to 2^10000.

%C No additional terms < 2^500000. - _Chai Wah Wu_, May 22 2016

%C No additional terms < 2^(10^10). - _Michael S. Branicky_, Apr 16 2023

%t Select[2^Range[0, 50000], Total@ Pick[DigitCount@ #, {1, 0, 1, 0, 1, 0, 1, 0, 1, 0}, 1] == 1 &] (* _Michael De Vlieger_, May 04 2016 *)

%t od1Q[n_]:=Count[IntegerDigits[n],_?(OddQ[#]&)]==1; Select[2^Range[0,100],od1Q] (* _Harvey P. Dale_, Sep 04 2024 *)

%o (Ruby)

%o ary = [1]

%o s = 1

%o (1..10 ** 4).each{|i|

%o s *= 2

%o j = s.to_s.split('').map(&:to_i).select{|i| i % 2 == 1}.size

%o ary << s if j == 1

%o }

%o p ary

%Y Cf. A068994, A272698.

%K nonn,base

%O 1,2

%A _Seiichi Manyama_, May 04 2016