login
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.
0
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
1,1
COMMENTS
Balanced isolated numbers (of order two): 18, 30, 192, 312, ..
FORMULA
a(n) = A167706(k) = (A167706(k-1) + A167706(k+1))/2.
EXAMPLE
a(1) = A167706(2) = (A167706(2-1) + A167706(2+1))/2 = (2 + 6)/2 = 4.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved