A326777 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the area of the triangle ((n, a(n)), (n+1, a(n+1)), (n+2, a(n+2))) is unique.

1, 2, 3, 5, 4, 7, 8, 14, 6, 9, 18, 10, 11, 19, 12, 13, 24, 15, 22, 16, 28, 17, 25, 21, 38, 20, 26, 54, 23, 29, 60, 27, 30, 59, 31, 32, 61, 34, 37, 67, 35, 36, 68, 33, 39, 77, 40, 41, 76, 42, 47, 92, 43, 44, 87, 45, 46, 91, 48, 50, 98, 49, 51, 100, 53, 55, 105

Offset

1,2

Comments

For any n > 0, the area of the triangle ((n, a(n)), (n+1, a(n+1)), (n+2, a(n+2))) equals abs(2*a(n+1) - a(n) - a(n+2)).

This sequence has similarities with A081145; here the absolute value of the second difference is unique, there the absolute value of the first difference.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..1000

Rémy Sigrist, PARI program for A326777

Example

The first terms, alongside the area of the n-th triangle, are:
  n   a(n)  Area
  --  ----  ----
   1     1     0
   2     2     1
   3     3     3
   4     5     4
   5     4     2
   6     7     5
   7     8    14
   8    14    11
   9     6     6
  10     9    17
  11    18     9
  12    10     7
  13    11    15

Prog

(PARI) See Links section.

Crossrefs

Cf. A081145.

Sequence in context: A099424 A117955 A074049 * A193973 A245057 A127521

Adjacent sequences: A326774 A326775 A326776 * A326778 A326779 A326780

Keyword

nonn

Author

Rémy Sigrist, Jul 29 2019

Status

approved