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

0, 1, 3, 6, 11, 17, 25, 36, 50, 69, 92, 116, 141, 159, 185, 223, 256, 287, 340, 398, 445, 479, 536, 568, 596, 669, 767, 875, 969, 1078, 1154, 1225, 1292, 1338, 1502, 1658, 1764, 1917, 2012, 2105, 2272, 2468, 2640, 2754, 2837, 2955, 3204, 3429, 3648, 3888, 4147

Offset: 1

Author

Rémy Sigrist, Oct 27 2024

Keywords

• nonn

Comments

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).

This sequence is a variant of A101274 and A363446; here we consider alternating sums, there sums of consecutive terms.

By necessity, all terms are distinct.

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).

Examples

			The first terms, alongside the alternate sums of consecutive terms ending with a(n), are:
  n   a(n)  Alternating sums
  --  ----  -------------------------------------------
   1     0  0
   2     1  -1, 1
   3     3  2, -2, 3
   4     6  -4, 4, -3, 6
   5    11  7, -7, 8, -5, 11
   6    17  -10, 10, -9, 12, -6, 17
   7    25  15, -15, 16, -13, 19, -8, 25
   8    36  -21, 21, -20, 23, -17, 28, -11, 36
   9    50  29, -29, 30, -27, 33, -22, 39, -14, 50
  10    69  -40, 40, -39, 42, -36, 47, -30, 55, -19, 69
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..5000
• Rémy Sigrist, C++ program

Crossrefs

Cf. A101274, A363446.