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A128760
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Number of ways to write n as the absolute difference of a power of 2 and a power of 3.
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3
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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
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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