cp's OEIS Frontend

A128760 Number of ways to write n as the absolute difference of a power of 2 and a power of 3.

%I A128760 #4 Nov 16 2012 20:57:56
%S A128760 1,4,1,1,0,3,0,3,1,0,0,1,0,2,0,1,0,1,0,1,0,0,0,2,0,1,1,0,0,1,0,1,0,0,
%T A128760 0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,1,0,0,
%U A128760 0,0,0,0,0,1,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0
%N A128760 Number of ways to write n as the absolute difference of a power of 2 and a power of 3.
%C A128760 a(A014121(n)) > 0; the only even numbers m with a(m)>0 are of the form m=3^k-1: a(A024023(n)) > 0;
%C A128760 Conjecture: there exists c>=23 such that a(n)<2 for n>c.
%H A128760 Max Alekseyev, <a href="/A128760/b128760.txt">Table of n, a(n) for n = 0..1000</a>
%e A128760 a(1) = #{2^1 - 3^0, 2^2 - 3^1, 3^1 - 2^1, 3^2 - 2^3} = 4;
%e A128760 a(2) = #{3^1 - 2^0} = 1;
%e A128760 a(3) = #{2^2 - 3^0} = 1;
%e A128760 a(5) = #{2^3 - 3^1, 2^5 - 3^3, 3^2 - 2^2} = 3;
%e A128760 a(7) = #{2^3 - 3^0, 2^4 - 3^2, 3^2 - 2^1} = 3;
%e A128760 a(8) = #{3^2 - 2^0} = 1;
%e A128760 a(11) = #{3^3 - 2^4} = 1;
%e A128760 a(13) = #{2^4 - 3^1, 2^8 - 3^5} = 2;
%e A128760 a(15) = #{2^4 - 2^0} = 1;
%e A128760 a(17) = #{3^4 - 2^6} = 1;
%e A128760 a(19) = #{3^3 - 2^3} = 1;
%e A128760 a(23) = #{2^5 - 3^2, 3^3 - 2^2} = 2;
%e A128760 a(25) = #{3^3 - 2^1} = 1.
%Y A128760 Cf. A000079, A000244.
%K A128760 nonn
%O A128760 0,2
%A A128760 _Reinhard Zumkeller_, Mar 25 2007