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%I #13 Nov 20 2019 16:29:46
%S 0,1,-1,-3,2,7,12,11,10,9,8,13,18,23,28,33,19,5,-9,-23,-37,-51,-50,
%T -49,-48,-47,-46,-45,-44,-52,-60,-68,-76,-84,-92,-100,-108,-83,-58,
%U -33,-8,17,42,67,92,117,116,115,114,113,112,111,110,109,108,107,118,129
%N Sequence of distinct integers such that a(1) = 0, and for k = 1, 2, ..., the last term so far and the k next terms are in arithmetic progression with common difference d_k such that abs(d_k) is as small as possible and d_k > 0 iff k is odd.
%C The sequence zigzags and A000124 corresponds to the indices of its extrema.
%C Will this sequence change sign infinitely often?
%H Rémy Sigrist, <a href="/A329724/b329724.txt">Table of n, a(n) for n = 1..10012</a>
%H Rémy Sigrist, <a href="/A329724/a329724.txt">C++ program for A329724</a>
%H Rémy Sigrist, <a href="/A329724/a329724.png">Scatterplot of the first 39582754 terms</a>
%e The first terms, alongside the corresponding k and d_k, are:
%e n a(n) k d_k
%e -- ---- --- ---
%e 1 0 N/A N/A
%e 2 1 1 1
%e 3 -1 2 -2
%e 4 -3 2 -2
%e 5 2 3 5
%e 6 7 3 5
%e 7 12 3 5
%e 8 11 4 -1
%e 9 10 4 -1
%e 10 9 4 -1
%e 11 8 4 -1
%e 12 13 5 5
%e 13 18 5 5
%e 14 23 5 5
%e 15 28 5 5
%e 16 33 5 5
%o (C++) See Links section.
%Y Cf. A000124, A001057.
%K sign,look
%O 1,4
%A _Rémy Sigrist_, Nov 19 2019
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