Re: how to solve the integer equation Abs[3^x-2^y]=1
- To: mathgroup at smc.vnet.net
- Subject: [mg103213] Re: how to solve the integer equation Abs[3^x-2^y]=1
- From: a boy <a.dozy.boy at gmail.com>
- Date: Thu, 10 Sep 2009 07:24:26 -0400 (EDT)
- References: <200909031110.HAA24198@smc.vnet.net> <h7tbeb$fs6$1@smc.vnet.net>
running codes:
Gap = Function[k, x = k*Log[2, 3];
Min[3^k - 2^Floor[x], 2^Ceiling[x] - 3^k]];
orderedlogs = Ordering[Table[Log[N[Gap[n]]], {n, 1, 50000}]];
With[{sublists = Split[orderedlogs, #1 >= #2 &]},
With[{m = Max[Length /@ sublists]},
Select[sublists, Length[#] == m &]]]
I have found these trios:
{{665, 660, 659}, {1330, 1325, 1324}, {1995, 1990, 1989}, {2660, 2655,
2654}, {12941, 12936, 12935}, {13606, 13601, 13600}, {14271, 14266,
14265}, {14936, 14931, 14930}, {16931, 16926, 16925}, {17596,
17591, 17590}, {18261, 18256, 18255}, {18926, 18921, 18920}, {29207,
29202, 29201}, {29872, 29867, 29866}, {30537, 30532,
30531}, {31202, 31197, 31196}, {32532, 32527, 32526}, {33197, 33192,
33191}, {33862, 33857, 33856}, {34527, 34522, 34521}, {44808,
44803, 44802}, {45473, 45468, 45467}, {46138, 46133, 46132}, {46803,
46798, 46797}, {48133, 48128, 48127}, {48798, 48793,
48792}, {49463, 49458, 49457}}
- References:
- how to solve the integer equation Abs[3^x-2^y]=1
- From: a boy <a.dozy.boy@gmail.com>
- how to solve the integer equation Abs[3^x-2^y]=1