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 A260873 Lexicographically first sequence of positive integers, every nonempty subset of which has a distinct mean. 1
 1, 2, 4, 8, 16, 32, 104, 321, 1010, 3056, 9477, 29437, 91060, 286574, 919633 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The seeming pattern a(n) = 2^(n-1) is broken at a(7)=104. Can the value of lim_{n->inf.} a(n)/a(n-1) be determined? LINKS Manfred Scheucher, Sage Script Manfred Scheucher, Sage Script#2 EXAMPLE {1} has only 1 nonempty subset, {1}; its mean is 1. {1,2} has 3 nonempty subsets, {1}, {2}, and {1,2}; their means are 1, 2, and 3/2, respectively. {1,2,3} has 7 nonempty subsets, not all of which have distinct means: {2}, {1,3}, and {1,2,3} all have a mean of 2. Therefore, a(3) > 3. {1,2,4} has 7 nonempty subsets, {1}, {2}, {4}, {1,2}, {1,4}, {2,4} and {1,2,4}, all of which have distinct means, so a(3)=4. For the set {1,2,4,5}, the subsets {1,5} and {2,4} have the same mean; for {1,2,4,6}, {4} and {2,6} have the same mean; and for {1,2,4,7}, {4} and {1,7} have the same mean; but all nonempty subsets of {1,2,4,8} are distinct, so a(4)=8. For each k in 9 <= k <= 15, there are at least two subsets of {1,2,4,8,k} having the same mean, but all nonempty subsets of {1,2,4,8,16} have distinct means, so a(5)=16. CROSSREFS Cf. A259544. Sequence in context: A264656 A078227 A250073 * A138814 A233424 A137181 Adjacent sequences:  A260870 A260871 A260872 * A260874 A260875 A260876 KEYWORD nonn,more,hard AUTHOR Jon E. Schoenfield, Aug 01 2015 EXTENSIONS a(11)-a(13) from Manfred Scheucher, Aug 04 2015 a(14)-a(15) from Manfred Scheucher, Aug 09 2015 STATUS approved

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Last modified June 24 21:16 EDT 2019. Contains 324337 sequences. (Running on oeis4.)