A272698 Powers of 2 with exactly one even decimal digit.

2, 4, 8, 16, 32, 512

Offset

1,1

Comments

The number of even digits of powers of 2 is more than 0. However, it seems there are few powers of 2 with 1 even digit.

If there are any other terms in this sequence, they are greater than 2^10^10. - Charles R Greathouse IV, May 04 2016

Links

Table of n, a(n) for n=1..6.

Mathematica

Select[2^Range[0, 50000], Total@ Pick[DigitCount@ #, {0, 1, 0, 1, 0, 1, 0, 1, 0, 1}, 1] == 1 &] (* Michael De Vlieger, May 04 2016 *)
Select[2^Range[200], Count[IntegerDigits[#], _?EvenQ]==1&] (* Harvey P. Dale, Aug 20 2017 *)

Prog

(Ruby)
ary = []
s = 1
(1..10 ** 4).each{|i|
  s *= 2
  j = s.to_s.split('').map(&:to_i).select{|i| i % 2 == 0}.size
  ary << s if j == 1
}
p ary
(PARI) is(n)=my(d=digits(n)); n>1 && n>>valuation(n, 2)==1 && sum(i=1, #d, d[i]%2==0)==1 \\ Charles R Greathouse IV, May 04 2016

Crossrefs

Sequence in context: A138814 A233424 A137181 * A355548 A036373 A119610

Adjacent sequences: A272695 A272696 A272697 * A272699 A272700 A272701

Keyword

nonn,base

Author

Seiichi Manyama, May 04 2016

Status

approved