A272898 Numbers k such that 2^k has equal numbers of odd and even decimal digits.

4, 5, 13, 30, 51, 64, 65, 77, 78, 130, 144, 171, 185, 199, 210, 239, 259, 263, 271, 296, 312, 369, 389, 391, 429, 437, 449, 457, 483, 490, 496, 498, 502, 551, 582, 583, 628, 648, 677, 709, 721, 744, 750, 776, 796, 874, 923, 943

Offset: 1

Author

Seiichi Manyama, May 09 2016

Keywords

• nonn
• base

Examples

			4 is a term since 2^4 = 16 has 1 odd digit and 1 even digit.
12 is not a term since 4096 has 1 odd digit and 3 even digits.
13 is a term since 8192 has 2 odd digits and 2 even digits.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000079.

Programs

Mathematica

ok[n_] := Block[{d=IntegerDigits[2^n]}, EvenQ@ Length@ d && 0 == Plus @@ ((-1)^d) ]; Select[ Range@ 10000, ok] (* Giovanni Resta, May 09 2016 *)

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