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

Author

Gus Wiseman, Sep 13 2019

Keywords

• nonn

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.

Examples

			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
		

Crossrefs

Numbers whose binary indices have integer mean are A326669.

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

Programs

Mathematica

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