A280007 Balanced single (or balanced isolated) numbers (of order one): single (or isolated) numbers which are the average of the previous single (or isolated) number and the following single (or isolated) number.
4, 12, 30, 42, 60, 228, 257, 270, 312, 373, 462, 570, 600, 733, 858, 882, 947, 977, 1092, 1103, 1123, 1187, 1230, 1290, 1302, 1367, 1428, 1511, 1620, 1747, 1753, 1907, 1998, 2028, 2287, 2340, 2417, 2550, 2677, 2688, 2730, 2903, 3313, 3319, 3540, 3582, 3637, 3733, 4020
Offset: 1
Keywords
Examples
a(1) = A167706(2) = (A167706(2-1) + A167706(2+1))/2 = (2 + 6)/2 = 4.
Programs
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Mathematica
With[{nn = 560}, Function[s, Part[s, #] & /@ Select[Range[Length@ s - 1], Mean@{s[[# - 1]], s[[# + 1]]} == s[[#]] &]]@ Prepend[Union[Transpose[ Select[Partition[Prime@ Range@ nn, 3, 1], And[#[[2]] - #[[1]] != 2, #[[3]] - #[[2]] != 2] &]][[2]], Map[Mean, Select[Partition[Prime@ Range@ nn, 2, 1], Differences@ # == {2} &]]], 2]] (* Michael De Vlieger, Feb 22 2017, after Harvey P. Dale at A007510 and A014574 *)
Comments