A237545 Odious powers of 3.

1, 81, 2187, 59049, 177147, 1594323, 14348907, 43046721, 1162261467, 3486784401, 31381059609, 22876792454961, 68630377364883, 205891132094649, 16677181699666569, 150094635296999121, 36472996377170786403, 328256967394537077627, 8862938119652501095929, 79766443076872509863361

Offset: 1

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Feb 09 2014

Keywords

• nonn
• easy

Comments

Intersection of A000069 and A000244.

Exponents of a(n): A223024.

It seems that this sequence includes about half of the powers of 3. For example, a(50171) = 3^99999. - Charles R Greathouse IV, Mar 05 2014

Links

• Robert Israel, Table of n, a(n) for n = 1..1058

Crossrefs

Cf. A000069 (odious numbers), A000244 (powers of 3), A223024.

Programs

Maple

select(t -> convert(convert(t,base,2),`+`)::odd, [seq(3^i,i=0..100)]); # Robert Israel, Oct 10 2016

Mathematica

Select[3^Range[32],OddQ[First[DigitCount[#,2] ] ]&] (* Wouter Meeussen, Feb 09 2014 *)

PARI

for(n=0,100,if(hammingweight(t=3^n)%2,print1(t", "))) \\ Charles R Greathouse IV, Mar 05 2014

Extensions

Corrected and more terms added by Robert Israel, Oct 10 2016