A330004 a(1) = 0, and for n > 0, a(n+1) = u - v where u (resp. v) is the number of terms equal to a(n) (resp. a(n)+1) among the first n terms.

0, 1, 1, 2, 1, 2, 2, 3, 1, 1, 2, 3, 2, 3, 3, 4, 1, 1, 2, 2, 3, 4, 2, 3, 4, 3, 4, 4, 5, 1, 0, -6, 1, 1, 2, 2, 3, 3, 4, 5, 2, 2, 3, 4, 5, 3, 4, 5, 4, 5, 5, 6, 1, -1, -1, 0, -8, 1, 0, -8, 2, 2, 3, 3, 4, 4, 5, 6, 2, 2, 3, 3, 4, 5, 6, 3, 4, 5, 6, 4, 5, 6, 5, 6, 6

Offset: 1

Author

Rémy Sigrist, Nov 26 2019

Keywords

• sign
• look

Comments

The sequence has chaotic features (see plot in Links section).

Examples

			The first terms, alongside u and v, are:
  n   a(n)  u  v
  --  ----  -  -
   1     0  1  0
   2     1  1  0
   3     1  2  0
   4     2  1  0
   5     1  3  1
   6     2  2  0
   7     2  3  0
   8     3  1  0
   9     1  4  3
  10     1  5  3
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Density plot of the first 25000000 terms

Crossrefs

See A329981 for similar sequences.

Programs

PARI

for (n=1, #(a=vector(85)), print1 (a[n]=if (n==1, 0, sum(k=1, n-1, (a[k]==a[n-1])-(a[k]==a[n-1]+1)))", "))