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%I #14 Jul 27 2019 14:57:51
%S 0,1,3,11,139,32907,2147516555,9223372039002292363,
%T 170141183460469231740910675754886398091,
%U 57896044618658097711785492504343953926805133516280751251469702679711451218059
%N a(0) = 0, a(n) = Sum_{i=0..n-1} 2^((2^i)-1).
%C Maximum position in A072644 where the value n occurs.
%C Also partial sums of A058891, i.e. the first differences are there. - _R. J. Mathar_, May 15 2007
%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. We define the set-system with BII-number n to be obtained by taking the binary indices of each binary index of n. Every finite set of finite nonempty sets has a different BII-number. For example, 18 has reversed binary expansion (0,1,0,0,1), and since the binary indices of 2 and 5 are {2} and {1,3} respectively, the BII-number of {{2},{1,3}} is 18. Then a(n) is the minimum BII-number of a set-system with n distinct vertices. - _Gus Wiseman_, Jul 24 2019
%p A072639 := proc(n) local i; add(2^((2^i)-1),i=0..(n-1)); end;
%t a[n_] := Sum[2^(2^i - 1), {i, 0, n - 1}]; Table[a[n], {n, 0, 9}] (* _Jean-François Alcover_, Mar 06 2016 *)
%o (PARI) a(n) = if (n, sum(i=0, n-1, 2^((2^i)-1)), 0); \\ _Michel Marcus_, Mar 06 2016
%Y Binary width of each term: A000079. Cf. A072638, A072640, A072654.
%Y Cf. A058891.
%Y Cf. A000120, A014221, A029931, A034797, A048793, A070939, A326031, A326702.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jun 02 2002
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