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A380968 Lexicographically earliest sequence of positive integers such that for any value k, no two sets of one or more indices at which k occurs have the same mean.

%I A380968 #14 Feb 12 2025 21:40:24
%S A380968 1,1,2,1,2,2,3,1,3,3,2,4,4,5,3,1,4,5,5,6,6,7,4,6,7,2,5,8,6,3,7,1,7,5,
%T A380968 8,8,4,9,8,9,9,10,10,6,10,9,11,11,10,11,2,8,12,11,3,7,10,12,5,12,9,11,
%U A380968 4,13,13,14,13,12,6,14,13,14,10,15,15,16,15,11,13
%N A380968 Lexicographically earliest sequence of positive integers such that for any value k, no two sets of one or more indices at which k occurs have the same mean.
%C A380968 A260873 gives the indices of 1s in the sequence.
%C A380968 The longest run in the sequence has length 2.
%C A380968 No three equal terms will appear at indices in arithmetic progression.
%C A380968 For any value k, the distances between pairs of k will be distinct.
%H A380968 Neal Gersh Tolunsky, <a href="/A380968/b380968.txt">Table of n, a(n) for n = 1..10000</a>
%e A380968 a(7) = 3: a(7) cannot be 1 because i = 4; i = 1,7; and i = 1,4,7 would all have the same mean index 4. a(7) cannot be 2 because i = 6; i = 5,6,7; and i = 5,7 would have the same mean index 6. So a(7) = 3.
%e A380968 a(19) cannot be 1, 2, or 3. a(19) = 4 does not work either because i = 13,19 would have the same mean (namely 16) as i = 12,17,19. So a(19) = 5.
%Y A380968 Cf. A380783, A380751.
%K A380968 nonn
%O A380968 1,3
%A A380968 _Neal Gersh Tolunsky_, Feb 09 2025