A072639 a(0) = 0, a(n) = Sum_{i=0..n-1} 2^((2^i)-1).

0, 1, 3, 11, 139, 32907, 2147516555, 9223372039002292363, 170141183460469231740910675754886398091, 57896044618658097711785492504343953926805133516280751251469702679711451218059

Offset: 0

Author

Antti Karttunen, Jun 02 2002

Keywords

• nonn

Comments

Maximum position in A072644 where the value n occurs.

Also partial sums of A058891, i.e. the first differences are there. - R. J. Mathar, May 15 2007

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

Crossrefs

Binary width of each term: A000079. Cf. A072638, A072640, A072654.

Cf. A058891.

Cf. A000120, A014221, A029931, A034797, A048793, A070939, A326031, A326702.

Programs

Maple

A072639 := proc(n) local i; add(2^((2^i)-1),i=0..(n-1)); end;

Mathematica

a[n_] := Sum[2^(2^i - 1), {i, 0, n - 1}]; Table[a[n], {n, 0, 9}] (* Jean-François Alcover, Mar 06 2016 *)

PARI

a(n) = if (n, sum(i=0, n-1, 2^((2^i)-1)), 0); \\ Michel Marcus, Mar 06 2016