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A266153
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Least positive integer y such that -n = x^4 - y^3 + z^2 for some positive integers x and z, or 0 if no such y exists.
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13
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3, 3, 2, 6, 13, 2, 3, 5, 5, 3, 28, 4, 15, 4, 10, 33, 3, 7, 5, 238, 31, 3, 4, 5, 3, 11, 4, 5, 21, 11, 6, 4, 17, 11, 5, 98, 7, 4, 4, 5, 147, 19, 5, 4, 5, 6, 4, 29, 75, 1011, 7, 9, 7, 4, 8, 6, 59, 47, 4, 5, 71, 4, 17, 45, 13, 7, 18, 9, 175, 8
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OFFSET
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1,1
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COMMENTS
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The conjecture in A266152 implies that a(n) > 0 for all n > 0.
It seems that a(n) < n*(n+4)/2 for all n > 1.
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LINKS
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EXAMPLE
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a(1) = 3 since -1 = 1^4 - 3^3 + 5^2.
a(2) = 3 since -2 = 2^4 - 3^3 + 3^2.
a(11) = 28 since -11 = 5^4 - 28^3 + 146^2.
a(20) = 238 since -20 = 32^4 - 238^3 + 3526^2.
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MATHEMATICA
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SQ[n_]:=SQ[n]=n>0&&IntegerQ[Sqrt[n]]
Do[y=Floor[n^(1/3)]+1; Label[bb]; Do[If[SQ[-n+y^3-x^4], Print[n, " ", y]; Goto[aa]], {x, 1, (-n+y^3)^(1/4)}]; y=y+1; Goto[bb]; Label[aa]; Continue, {n, 1, 70}]
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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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