A330403 Lexicographically earliest sequence of distinct positive terms with an associate sequence t such that t(0) = 0, and for any n > 0, at least one of t(n-1) - a(n) or t(n-1) + a(n) is a square; in case t(n-1) - a(n) is a square, set t(n) = t(n-1) - a(n), otherwise set t(n) = t(n-1) + a(n).

1, 3, 4, 9, 5, 12, 7, 8, 15, 16, 25, 11, 13, 24, 21, 32, 20, 33, 40, 27, 28, 17, 19, 36, 39, 56, 45, 35, 48, 49, 64, 55, 72, 63, 23, 57, 60, 77, 65, 84, 44, 52, 29, 31, 68, 37, 80, 41, 76, 99, 81, 95, 51, 69, 87, 105, 123, 43, 88, 47, 92, 141, 96, 129, 111, 93

Offset: 1

Author

Rémy Sigrist, Dec 13 2019

Keywords

• nonn

Comments

This sequence is a variant of A330385.

Examples

			The first terms, alongside t(n), are:
  n   a(n)  t(n)
  --  ----  ----
   0  N/A      0
   1     1     1
   2     3     4
   3     4     0
   4     9     9
   5     5     4
   6    12    16
   7     7     9
   8     8     1
   9    15    16
  10    16     0
  11    25    25
  12    11    36
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A330403

Crossrefs

See A330401 for similar sequences.

Cf. A330385, A330422 (running totals).

Programs

PARI

See Links section.