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

1,3

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).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..5000

Rémy Sigrist, C++ program

Example

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

Prog

(C++) // See Links section.

Crossrefs

Cf. A101274, A363446.

Sequence in context: A119639 A281376 A247586 * A107957 A000603 A003453

Adjacent sequences: A377404 A377405 A377406 * A377408 A377409 A377410

Keyword

nonn

Author

Rémy Sigrist, Oct 27 2024

Status

approved