A380174 a(n) is the least integer (in absolute value) not among the n initial terms of A377091; in case of a tie, preference is given to the positive value.

0, 1, -1, -1, -1, 3, -3, -3, -3, -3, -5, -5, -5, -5, -5, -5, -5, 9, 9, 9, 9, 9, 9, 10, 11, 12, -13, 14, 14, 14, 14, 14, 14, 14, 15, 16, 17, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 22, 22, 24, 24, 24, 24, -25, -26, -27, -28, 29, 29, 29, 29, 29, 29, 29, 29, 33

Offset: 0

Author

Rémy Sigrist, Jan 15 2025

Keywords

• sign

Comments

If abs(A377091(n-1) - a(n)) is a square number for some n > 0, then A377091(n) = a(n).

Examples

			The initial terms are:
  n   a(n)  n initial terms of A377091
  --  ----  ----------------------------------
   0     0  {}
   1     1  {0}
   2    -1  {0, 1}
   3    -1  {0, 1, 2}
   4    -1  {-2, 0, 1, 2}
   5     3  {-2, -1, 0, 1, 2}
   6    -3  {-2, -1, 0, 1, 2, 3}
   7    -3  {-2, -1, 0, 1, 2, 3, 4}
   8    -3  {-2, -1, 0, 1, 2, 3, 4, 5}
   9    -3  {-4, -2, -1, 0, 1, 2, 3, 4, 5}
  10    -5  {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, PARI program

Crossrefs

See A379067 and A379068 for similar sequences.

Cf. A377091.

Programs

PARI

\\ See Links section.

Formula

abs(a(n)) = min(A379067(n-1), A379068(n-1)) for any n > 0.