cp's OEIS Frontend

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

%I A327478 #6 Sep 13 2019 17:05:05
%S A327478 1,2,4,7,8,14,16,21,28,31,32,39,42,56,57,62,64,73,78,84,93,107,112,
%T A327478 114,124,127,128,141,146,155,156,168,175,177,186,214,217,224,228,245,
%U A327478 248,254,256,267,273,282,287,292,310,312,313,336,341,350,354,371,372
%N A327478 Numbers whose average binary index is also a binary index.
%C A327478 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.
%e A327478 The sequence of terms together with their binary indices begins:
%e A327478    1: 1
%e A327478    2: 2
%e A327478    4: 3
%e A327478    7: 1 2 3
%e A327478    8: 4
%e A327478   14: 2 3 4
%e A327478   16: 5
%e A327478   21: 1 3 5
%e A327478   28: 3 4 5
%e A327478   31: 1 2 3 4 5
%e A327478   32: 6
%e A327478   39: 1 2 3 6
%e A327478   42: 2 4 6
%e A327478   56: 4 5 6
%e A327478   57: 1 4 5 6
%e A327478   61: 2 3 4 5 6
%t A327478 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A327478 Select[Range[100],MemberQ[bpe[#],Mean[bpe[#]]]&]
%Y A327478 Numbers whose binary indices have integer mean are A326669.
%Y A327478 Cf. A000016, A000120, A029931, A048793, A065795, A070939, A237984, A240850, A327473, A327474, A327481.
%K A327478 nonn
%O A327478 1,2
%A A327478 _Gus Wiseman_, Sep 13 2019