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%I #23 Jul 15 2023 14:02:25
%S 4,5,13,30,51,64,65,77,78,130,144,171,185,199,210,239,259,263,271,296,
%T 312,369,389,391,429,437,449,457,483,490,496,498,502,551,582,583,628,
%U 648,677,709,721,744,750,776,796,874,923,943
%N Numbers k such that 2^k has equal numbers of odd and even decimal digits.
%H Seiichi Manyama, <a href="/A272898/b272898.txt">Table of n, a(n) for n = 1..1000</a>
%e 4 is a term since 2^4 = 16 has 1 odd digit and 1 even digit.
%e 12 is not a term since 4096 has 1 odd digit and 3 even digits.
%e 13 is a term since 8192 has 2 odd digits and 2 even digits.
%t ok[n_] := Block[{d=IntegerDigits[2^n]}, EvenQ@ Length@ d && 0 == Plus @@ ((-1)^d) ]; Select[ Range@ 10000, ok] (* _Giovanni Resta_, May 09 2016 *)
%o (PARI) is(n)=my(d=digits(2^n)); #d%2==0 && sum(i=1,#d,(-1)^d[i])==0 \\ _Charles R Greathouse IV_, May 09 2016
%Y Cf. A000079.
%K nonn,base
%O 1,1
%A _Seiichi Manyama_, May 09 2016
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