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A273594
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Least number k such that abs(A011541(n+1) - A011541(n)*k^3) is a minimum.
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0
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OFFSET
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1,1
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COMMENTS
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If b is the sum of two positive cubes in exactly n ways, then b*c^3 is the sum of two positive cubes in at least n ways for all c > 0. So A011541(i)*c^3 is a candidate for unknown Taxi-cab numbers. a(6) = 79 is an interesting example that is related to this case. Additionally, the benefit of this simple fact is the determination of upper bounds for unknown Taxi-cab numbers in relatively easy way.
The inequalities that are given in the comment section of A011541 are:
So a(6) <= 101, a(7) <= 127, a(8) <= 139.
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LINKS
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EXAMPLE
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a(5) = 79 because abs(A011541(6) - A011541(5)*79^3) = abs(24153319581254312065344 - 48988659276962496*79^3) = 0
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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