A379675 a(0) = 0, and for any n > 0, a(n) is the least integer (in absolute value) not yet in the sequence such that the absolute difference of a(n-1) and a(n) is a square and a(n) is positive iff n is odd.

0, 1, -3, 6, -10, 15, -1, 3, -6, 10, -15, 21, -4, 5, -11, 14, -2, 2, -7, 9, -16, 20, -5, 4, -12, 13, -23, 26, -38, 11, -14, 22, -27, 37, -44, 56, -8, 8, -17, 19, -30, 34, -47, 17, -19, 30, -34, 47, -53, 28, -21, 43, -57, 7, -9, 16, -20, 29, -35, 46, -18, 18

Offset

0,3

Comments

This sequence is a variant of A377091 where, beyond the initial term a(0) = 0, the sign of the terms alternates.

Will every integer appear in the sequence?

Links

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

Rémy Sigrist, Colored scatterplot of the sequence for n = 0..10000 (where the color is function of Sum_{k = 0..n-1} sign(a(k+1)-a(k)) * sqrt(abs(a(k+1)-a(k))))

Rémy Sigrist, PARI program

Example

The first terms are:
  n   a(n)  |a(n)-a(n-1)|
  --  ----  -------------
   0     0  N/A
   1     1  1^2
   2    -3  2^2
   3     6  3^2
   4   -10  4^2
   5    15  5^2
   6    -1  4^2
   7     3  2^2
   8    -6  3^2
   9    10  4^2
  10   -15  5^2
  11    21  6^2
  12    -4  5^2
  13     5  3^2
  14   -11  4^2

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A277616, A377091.

Sequence in context: A049989 A330258 A197056 * A104619 A194037 A194101

Adjacent sequences: A379672 A379673 A379674 * A379676 A379677 A379678

Keyword

sign

Author

Rémy Sigrist, Dec 29 2024

Status

approved