A066486 a(n) = min( x : x^3 + n^3 == 0 mod (x+n-1) ).
1, 6, 17, 34, 57, 2, 121, 6, 23, 262, 321, 386, 55, 534, 617, 88, 3, 902, 61, 144, 77, 52, 9, 1634, 1777, 1926, 17, 2242, 2409, 344, 2761, 198, 3137, 4, 3537, 164, 535, 4182, 4409, 112, 93, 5126, 5377, 768, 413, 6166, 453, 920, 7009, 7302, 1043, 22, 8217, 224, 13, 9186, 5, 34, 10209, 188, 19, 1560, 11657
Offset: 1
Keywords
Crossrefs
Cf. A066333.
Programs
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Mathematica
a[n_] := For[x = 1, True, x++, If[Mod[x^3 + n^3, x + n - 1] == 0, Return[x]]]; Array[a, 24] (* Jean-François Alcover, Feb 17 2018 *)
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PARI
a(n) = {my(k=1); while((k^3+n^3)%(k+n-1) != 0, k++); k; } \\ Altug Alkan, Feb 17 2018
Formula
a(n) = 3*n^2 - 4*n + 2 for n=1, 2, 3, 4, 5, 7, 10, 11, 12, 14, 15, 18, 24, 25, 26, 28, 29, 31, 33, 35, 38, ...
That is, in those cases a(n) = A056109(n-1). It appears that the corresponding indices are given by A133431 (i.e., 1 U A002504). - Michel Marcus, Feb 17 2018
Extensions
More terms from Altug Alkan, Feb 17 2018