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

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, 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, 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

Offset

0,2

Comments

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;

Conjecture: there exists c>=23 such that a(n)<2 for n>c.

Links

Max Alekseyev, Table of n, a(n) for n = 0..1000

Example

a(1) = #{2^1 - 3^0, 2^2 - 3^1, 3^1 - 2^1, 3^2 - 2^3} = 4;
a(2) = #{3^1 - 2^0} = 1;
a(3) = #{2^2 - 3^0} = 1;
a(5) = #{2^3 - 3^1, 2^5 - 3^3, 3^2 - 2^2} = 3;
a(7) = #{2^3 - 3^0, 2^4 - 3^2, 3^2 - 2^1} = 3;
a(8) = #{3^2 - 2^0} = 1;
a(11) = #{3^3 - 2^4} = 1;
a(13) = #{2^4 - 3^1, 2^8 - 3^5} = 2;
a(15) = #{2^4 - 2^0} = 1;
a(17) = #{3^4 - 2^6} = 1;
a(19) = #{3^3 - 2^3} = 1;
a(23) = #{2^5 - 3^2, 3^3 - 2^2} = 2;
a(25) = #{3^3 - 2^1} = 1.

Crossrefs

Cf. A000079, A000244.

Sequence in context: A278987 A135302 A364026 * A057884 A329637 A276834

Adjacent sequences: A128757 A128758 A128759 * A128761 A128762 A128763

Keyword

nonn

Author

Reinhard Zumkeller, Mar 25 2007

Status

approved