[seqfan] A077057 and A077058

Jean-François Alcover jf.alcover at gmail.com
Wed Oct 3 12:45:54 CEST 2012


Dear SeqFans,

I'm checking A077057 and A077058 with Mathematica,
and I get a few cases where the equation seems not to hold :

aa = A077057 =
{1, 2, 5, 3, 3, 27, 7, 37, 3, 4, 171, 22, 9, 14,
 1193, 5, 5, 553, 16, 6173, 11, 45, 143, 849, 6, 6, 18339,
 94, 1893, 103, 13, 33, 2001, 115, 12703, 7, 7, 67115,
 701, 73, 59, 1891117, 15, 551427, 23, 49771, 39, 4105015,
 8, 8, 24673, 41, 75585293, 22, 9095891, 989, 17};

bb = A077058 =
{1, 1, 2, 1, 1, 8, 2, 10, 1, 1, 40, 5, 2, 3, 250,
 1, 1, 106, 3, 1138, 2, 8, 25, 146, 1, 1, 2968, 15, 298, 16,
 2, 5, 352, 17, 1856, 1, 1, 9384, 97, 10, 8, 253970, 2,
 72664, 3, 6440, 5, 521904, 1, 1, 3034, 5, 9148450, 3,
 1084152, 117, 2};

g[n_] := Ceiling[Sqrt[n]] + n - 1;

t = Table[{n, aa[[n]], bb[[n]],
 aa[[n]]^2 - aa[[n]]*bb[[n]] - g[n]*bb[[n]]^2}, {n, 1, 57}];

Select[t, Last[#] != 1 && Last[#] != -1 &]

{{9, 3, 1, -5}, {33, 2001, 352, -1408703}, {54, 22, 3, -131}}

Can someone explain ?

jfa



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