cp's OEIS Frontend

A273525 Start with the set {0, 1}. At each step replace the set with the set of means of all its nonempty subsets. a(n) is the size of the set after the n-th step.

%I A273525 #29 Aug 20 2022 02:24:28
%S A273525 2,3,5,15,875,603919253973
%N A273525 Start with the set {0, 1}. At each step replace the set with the set of means of all its nonempty subsets. a(n) is the size of the set after the n-th step.
%C A273525 2 * 10^6 < a(5) < 7 * 10^12 (see G. Martin's proof at Mathematics Stack Exchange).
%C A273525 The brute-force Mathematica program given below overflows for a(5).
%C A273525 a(5) = 603919253973 was computed by Japheth Lim (see Math.StackExchange link). -  _Vladimir Reshetnikov_, Aug 23 2016
%C A273525 Exactly the same sequence results from the arithmetic mean, geometric mean and harmonic mean, provided that the initial set consists of two distinct positive numbers.
%H A273525 Mathematics Stack Exchange, <a href="http://math.stackexchange.com/questions/1797607">Repeatedly taking mean values of non-empty subsets of a set: 2, 3, 5, 15, 875, ...</a>, May 23 2016.
%e A273525 Before the first step the set is {0, 1}, so a(0) = 2.
%e A273525 After the first step the set is {0, 1, 1/2}, so a(1) = 3.
%e A273525 After the second step the set is {0, 1, 1/2, 1/4, 3/4}, so a(2) = 5.
%t A273525 Length/@NestList[Union[Mean/@Rest@Subsets@#]&, {0, 1}, 4]
%K A273525 nonn,more,hard
%O A273525 0,1
%A A273525 _Vladimir Reshetnikov_, May 23 2016
%E A273525 a(5) from _Vladimir Reshetnikov_, Aug 23 2016