A346516 A variant of Van Eck's sequence: For n >= 0, a(n+1) is the result of combining by XOR the numbers k such that k < n and a(k) = a(n). Start with a(0)=0.

0, 0, 0, 1, 0, 3, 0, 7, 0, 1, 3, 5, 0, 9, 0, 5, 11, 0, 11, 16, 0, 26, 0, 14, 0, 24, 0, 0, 26, 21, 0, 1, 10, 0, 31, 0, 62, 0, 29, 0, 56, 0, 31, 34, 0, 54, 0, 26, 9, 13, 0, 52, 0, 6, 0, 50, 0, 4, 0, 60, 0, 6, 53, 0, 58, 0, 5, 4, 57, 0, 68, 0, 1, 21, 29, 38, 0

Offset

0,6

Comments

XOR denotes the bitwise XOR operator.

This sequence is unbounded, and contains infinitely many 0's.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Rémy Sigrist, Scatterplot of the first 2^20 terms

Example

The first terms, alongside the corresponding k's, are:
  n   a(n)  k's
  --  ----  --------------------
   0     0  None
   1     0  0
   2     0  0, 1
   3     1  None
   4     0  0, 1, 2
   5     3  None
   6     0  0, 1, 2, 4
   7     7  None
   8     0  0, 1, 2, 4, 6
   9     1  3
  10     3  5
  11     5  None
  12     0  0, 1, 2, 4, 6, 8
  13     9  None
  14     0  0, 1, 2, 4, 6, 8, 12
  15     5  11

Prog

(PARI) { p=vector(123); v=0; for (n=0, 76, print1(v", "); w=p[1+v]; p[1+v]=bitxor(p[1+v], n); v=w) }

Crossrefs

Cf. A181391, A348080.

Sequence in context: A137436 A099893 A135534 * A337767 A249904 A324875

Adjacent sequences: A346513 A346514 A346515 * A346517 A346518 A346519

Keyword

nonn,base

Author

Rémy Sigrist, Sep 27 2021

Status

approved