A327478 Numbers whose average binary index is also a binary index.

1, 2, 4, 7, 8, 14, 16, 21, 28, 31, 32, 39, 42, 56, 57, 62, 64, 73, 78, 84, 93, 107, 112, 114, 124, 127, 128, 141, 146, 155, 156, 168, 175, 177, 186, 214, 217, 224, 228, 245, 248, 254, 256, 267, 273, 282, 287, 292, 310, 312, 313, 336, 341, 350, 354, 371, 372

Offset

1,2

Comments

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

Links

Table of n, a(n) for n=1..57.

Example

The sequence of terms together with their binary indices begins:
   1: 1
   2: 2
   4: 3
   7: 1 2 3
   8: 4
  14: 2 3 4
  16: 5
  21: 1 3 5
  28: 3 4 5
  31: 1 2 3 4 5
  32: 6
  39: 1 2 3 6
  42: 2 4 6
  56: 4 5 6
  57: 1 4 5 6
  61: 2 3 4 5 6

Mathematica

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[100], MemberQ[bpe[#], Mean[bpe[#]]]&]

Crossrefs

Numbers whose binary indices have integer mean are A326669.

Cf. A000016, A000120, A029931, A048793, A065795, A070939, A237984, A240850, A327473, A327474, A327481.

Sequence in context: A004616 A322386 A309583 * A062846 A102824 A324588

Adjacent sequences: A327475 A327476 A327477 * A327479 A327480 A327481

Keyword

nonn

Author

Gus Wiseman, Sep 13 2019

Status

approved