A329984 a(1) = 0 and for n > 0, a(n+1) is the odd part of k where k is the number of terms equal to a(n) among the first n terms.

0, 1, 1, 1, 3, 1, 1, 5, 1, 3, 1, 7, 1, 1, 9, 1, 5, 1, 11, 1, 3, 3, 1, 13, 1, 7, 1, 15, 1, 1, 17, 1, 9, 1, 19, 1, 5, 3, 5, 1, 21, 1, 11, 1, 23, 1, 3, 3, 7, 3, 1, 25, 1, 13, 1, 27, 1, 7, 1, 29, 1, 15, 1, 31, 1, 1, 33, 1, 17, 1, 35, 1, 9, 3, 9, 1, 37, 1, 19, 1

Offset: 1

Author

Rémy Sigrist, Nov 26 2019

Keywords

• nonn
• look

Comments

In other words, for n > 0, a(n+1) = A000265(o(n)) where o is the ordinal transform of the sequence.

Examples

			The first terms, alongside their ordinal transform, are:
  n   a(n)  o(n)
  --  ----  ----
   1     0     1
   2     1     1
   3     1     2
   4     1     3
   5     3     1
   6     1     4
   7     1     5
   8     5     1
   9     1     6
  10     3     2
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Logarithmic scatterplot of the first 2^16 terms

Crossrefs

See A329981 for similar sequences.

Cf. A000265.

Programs

PARI

o=vector(38); v=0; for (n=1, 80, print1 (v", "); o[1+v]++; v=o[1+v]/2^valuation(o[1+v],2))