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A327478 Numbers whose average binary index is also a binary index. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 25 11:16 EDT 2021. Contains 348249 sequences. (Running on oeis4.)