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A377407 Lexicographically earliest sequence of nonnegative integers such that the alternating sums of consecutive terms are all distinct.

%I A377407 #10 Oct 28 2024 16:24:17
%S A377407 0,1,3,6,11,17,25,36,50,69,92,116,141,159,185,223,256,287,340,398,445,
%T A377407 479,536,568,596,669,767,875,969,1078,1154,1225,1292,1338,1502,1658,
%U A377407 1764,1917,2012,2105,2272,2468,2640,2754,2837,2955,3204,3429,3648,3888,4147
%N A377407 Lexicographically earliest sequence of nonnegative integers such that the alternating sums of consecutive terms are all distinct.
%C A377407 In other words, for any distinct nonempty intervals t..u and v..w, Sum_{i = t..u} a(i)*(-1)^(i-t) <> Sum_{j = v..w} a(j)*(-1)^(j-v).
%C A377407 This sequence is a variant of A101274 and A363446; here we consider alternating sums, there sums of consecutive terms.
%C A377407 By necessity, all terms are distinct.
%C A377407 This sequence is strictly increasing, for if d = a(n) - a(n+1) > 0, then d would have been a better choice for a(n).
%H A377407 Rémy Sigrist, <a href="/A377407/b377407.txt">Table of n, a(n) for n = 1..5000</a>
%H A377407 Rémy Sigrist, <a href="/A377407/a377407_1.txt">C++ program</a>
%e A377407 The first terms, alongside the alternate sums of consecutive terms ending with a(n), are:
%e A377407   n   a(n)  Alternating sums
%e A377407   --  ----  -------------------------------------------
%e A377407    1     0  0
%e A377407    2     1  -1, 1
%e A377407    3     3  2, -2, 3
%e A377407    4     6  -4, 4, -3, 6
%e A377407    5    11  7, -7, 8, -5, 11
%e A377407    6    17  -10, 10, -9, 12, -6, 17
%e A377407    7    25  15, -15, 16, -13, 19, -8, 25
%e A377407    8    36  -21, 21, -20, 23, -17, 28, -11, 36
%e A377407    9    50  29, -29, 30, -27, 33, -22, 39, -14, 50
%e A377407   10    69  -40, 40, -39, 42, -36, 47, -30, 55, -19, 69
%o A377407 (C++) // See Links section.
%Y A377407 Cf. A101274, A363446.
%K A377407 nonn
%O A377407 1,3
%A A377407 _Rémy Sigrist_, Oct 27 2024