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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.
1
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.
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
KEYWORD
nonn,more,hard
AUTHOR
EXTENSIONS
a(5) from Vladimir Reshetnikov, Aug 23 2016
STATUS
approved