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%I #20 Feb 23 2017 23:27:37
%S 4,12,30,42,60,228,257,270,312,373,462,570,600,733,858,882,947,977,
%T 1092,1103,1123,1187,1230,1290,1302,1367,1428,1511,1620,1747,1753,
%U 1907,1998,2028,2287,2340,2417,2550,2677,2688,2730,2903,3313,3319,3540,3582,3637,3733,4020
%N 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.
%C Balanced isolated numbers (of order two): 18, 30, 192, 312, ..
%F a(n) = A167706(k) = (A167706(k-1) + A167706(k+1))/2.
%e a(1) = A167706(2) = (A167706(2-1) + A167706(2+1))/2 = (2 + 6)/2 = 4.
%t 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 *)
%Y Cf. A007510, A014574, A167706, A167909.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Feb 21 2017
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