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