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.

2, 3, 5, 15, 875, 603919253973

Offset

0,1

Comments

2 * 10^6 < a(5) < 7 * 10^12 (see G. Martin's proof at Mathematics Stack Exchange).

The brute-force Mathematica program given below overflows for a(5).

a(5) = 603919253973 was computed by Japheth Lim (see Math.StackExchange link). - Vladimir Reshetnikov, Aug 23 2016

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.

Links

Table of n, a(n) for n=0..5.

Mathematics Stack Exchange, Repeatedly taking mean values of non-empty subsets of a set: 2, 3, 5, 15, 875, ..., May 23 2016.

Example

Before the first step the set is {0, 1}, so a(0) = 2.
After the first step the set is {0, 1, 1/2}, so a(1) = 3.
After the second step the set is {0, 1, 1/2, 1/4, 3/4}, so a(2) = 5.

Mathematica

Length/@NestList[Union[Mean/@Rest@Subsets@#]&, {0, 1}, 4]

Crossrefs

Sequence in context: A111183 A330821 A248827 * A274336 A192648 A219339

Adjacent sequences: A273522 A273523 A273524 * A273526 A273527 A273528

Keyword

nonn,more,hard

Author

Vladimir Reshetnikov, May 23 2016

Extensions

a(5) from Vladimir Reshetnikov, Aug 23 2016

Status

approved