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%I #3 Mar 30 2012 17:26:19
%S 8,27,64,243,512,2048,6561,16384,59049,131072,524288,1594323,4194304,
%T 14348907,33554432,129140163,268435456,1073741824,3486784401,
%U 8589934592,31381059609,68719476736,274877906944,847288609443,2199023255552
%N Terms in A006899 which are closer to the next term than to the previous one.
%C Next terms are: 17592186044416, 68630377364883, 140737488355328, 562949953421312, 1853020188851841, 4503599627370496, 16677181699666569, 36028797018963968, 144115188075855872, 450283905890997363, 1152921504606846976. Is the sequence infinite? Cf. A006899 Numbers of the form 2^i or 3^j.
%F A006899(n) - A006899(n-1) > A006899(n+1) - A006899(n)
%t un=Union[Flatten[Table[{2^n, 3^n}, {n, 60}]]];Do[If[un[[i]]-un[[i-1]]>un[[i+1]]-un[[i]], Print[un[[i]]]], {i, 2, Length[un]-1}]
%Y Cf. A006899.
%K nonn
%O 1,1
%A _Zak Seidov_, Jan 03 2006