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

1,1

Comments

Balanced isolated numbers (of order two): 18, 30, 192, 312, ..

Links

Table of n, a(n) for n=1..49.

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

Cf. A007510, A014574, A167706, A167909.

Sequence in context: A036895 A309297 A296645 * A061726 A067706 A008261

Adjacent sequences: A280004 A280005 A280006 * A280008 A280009 A280010

Keyword

nonn

Author

Juri-Stepan Gerasimov, Feb 21 2017

Status

approved