A350708 A variant of Van Eck's sequence where we start with the value 0, and then alternatively add values to the right and to the left; the sequence lists the values as they are added.

0, 0, 1, 0, 1, 1, 4, 0, 2, 0, 1, 3, 0, 6, 0, 1, 5, 0, 4, 6, 3, 16, 0, 4, 15, 0, 4, 4, 2, 10, 0, 4, 2, 2, 21, 0, 5, 10, 4, 6, 10, 35, 0, 6, 2, 6, 1, 18, 0, 3, 19, 0, 8, 0, 1, 4, 12, 0, 2, 7, 0, 6, 8, 5, 40, 0, 4, 14, 0, 4, 7, 65, 0, 2, 20, 0, 5, 20, 76, 0, 2

Offset

0,7

Comments

The construction described here gives a variant f of Van Eck's sequence with domain Z, and a(n) = f(A001057(n)).

When a value v has already appeared before, then the next value is the least distance to a similar value, otherwise the next value is 0.

Links

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

Rémy Sigrist, Scatterplot of (A001057(n), a(n)) for n <= 1000000

Rémy Sigrist, PARI program

Example

The first steps of the construction are as follows:
  n   a(n)  Values so far (including a(n))
  --  ----  -------------------------------
   0     0                 0
   1     0                 0  0
   2     1              1  0  0
   3     0              1  0  0  0
   4     1           1  1  0  0  0
   5     1           1  1  0  0  0  1
   6     4        4  1  1  0  0  0  1
   7     0        4  1  1  0  0  0  1  0
   8     2     2  4  1  1  0  0  0  1  0
   9     0     2  4  1  1  0  0  0  1  0  0
  10     1  1  2  4  1  1  0  0  0  1  0  0

Prog

(PARI) See Links section.

Crossrefs

Cf. A001057, A181391.

Sequence in context: A247703 A395754 A280639 * A319037 A067565 A243154

Adjacent sequences: A350705 A350706 A350707 * A350709 A350710 A350711

Keyword

nonn

Author

Rémy Sigrist, Mar 27 2022

Status

approved