A352792 a(n) is the number of numbers k < n such that A109812(k) < A109812(n).

0, 1, 2, 2, 4, 4, 6, 7, 5, 7, 10, 9, 11, 10, 14, 6, 15, 17, 15, 10, 20, 16, 22, 18, 22, 12, 26, 14, 28, 21, 28, 31, 23, 28, 33, 24, 29, 37, 22, 39, 26, 39, 30, 27, 41, 37, 45, 35, 47, 49, 28, 50, 52, 29, 51, 55, 41, 50, 58, 40, 49, 44, 52, 45, 54, 44, 53, 47

Offset: 1

Author

Rémy Sigrist, Apr 03 2022

Keywords

• nonn

Examples

			The initial values of a(n), b(n) = A109812(n), and the corresponding k's, are:
  n   a(n)  b(n)  k's
  --  ----  ----  ---------------------------------------------------
   1     0     1  []
   2     1     2  [1]
   3     2     4  [1, 2]
   4     2     3  [1, 2]
   5     4     8  [1, 2, 3, 4]
   6     4     5  [1, 2, 3, 4]
   7     6    10  [1, 2, 3, 4, 5, 6]
   8     7    16  [1, 2, 3, 4, 5, 6, 7]
   9     5     6  [1, 2, 3, 4, 6]
  10     7     9  [1, 2, 3, 4, 5, 6, 9]
  11    10    18  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
  12     9    12  [1, 2, 3, 4, 5, 6, 7, 9, 10]
  13    11    17  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12]
  14    10    14  [1, 2, 3, 4, 5, 6, 7, 9, 10, 12]
  15    14    32  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]
  16     6     7  [1, 2, 3, 4, 6, 9]
  17    15    24  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16]
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Scatterplot of the first 100000 terms
• Rémy Sigrist, C++ program

Crossrefs

Cf. A109812, A352204.

Formula

a(n) <= n-1 with equality iff n belongs to A352204.