A344264 When computing A229037, the value of the n-th term will add up to n-1 new constraints on the n-1 following terms; a(n) is the number of new constraints that the computation of A229037(n) brings.

0, 1, 2, 2, 2, 5, 5, 7, 7, 4, 4, 8, 3, 3, 9, 9, 16, 15, 9, 11, 12, 15, 15, 23, 12, 14, 23, 8, 7, 16, 6, 6, 15, 14, 26, 21, 5, 6, 10, 4, 4, 12, 11, 27, 24, 13, 19, 18, 34, 31, 49, 24, 28, 47, 46, 22, 19, 21, 23, 48, 18, 18, 44, 20, 39, 57, 47, 40, 38, 43, 46

Offset

1,3

Comments

Once A229037(n) has been computed, we have the following constraints:

- for k = 1..n-1, A229037(n + k) <> 2*A229037(n) - A229037(n - k),

- if 2*A229037(n) - A229037(n - k) <= 0, then we ignore this constraint,

- if 2*A229037(n) - A229037(n - k) = 2*A229037(n') - A229037(n' - k')

for some n' < n and k' < n' such that n + k = n' + k',

then we also ignore this constraint.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Scatterplot of the first 100000 terms

Rémy Sigrist, PARI program for A344264

Formula

a(n) < n.

Example

The first terms, alongside the corresponding value of A229037 (denoted by f(n)) and the new constraints, are:
  n  a(n)  f(n)  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19
  -  ----  ----  -  -  -  -  -  -  -  -  -  --  --  --  --  --  --  --  --  --  --
  1     0     1  .  .  .  .  .  .  .  .  .  .   .   .   .   .   .   .   .   .   .
  2     1     1  .  .  1  .  .  .  .  .  .  .   .   .   .   .   .   .   .   .   .
  3     2     2  .  .  .  3  3  .  .  .  .  .   .   .   .   .   .   .   .   .   .
  4     2     1  .  .  .  .  .  1  1  .  .  .   .   .   .   .   .   .   .   .   .
  5     2     1  .  .  .  .  .  .  .  1  1  .   .   .   .   .   .   .   .   .   .
  6     5     2  .  .  .  .  .  .  3  3  2   3   3  .   .   .   .   .   .   .   .
  7     5     2  .  .  .  .  .  .  .  2  3  .    2   3   3  .   .   .   .   .   .
  8     7     4  .  .  .  .  .  .  .  .  6   6   7   7   6   7   7  .   .   .   .
  9     7     4  .  .  .  .  .  .  .  .  .   4   6   6   7  .    6   7   7  .   .

Prog

(PARI) See Links section.

Crossrefs

Cf. A229037, A293866.

Sequence in context: A324925 A163946 A240500 * A308512 A308857 A244480

Adjacent sequences: A344261 A344262 A344263 * A344265 A344266 A344267

Keyword

nonn

Author

Rémy Sigrist, May 13 2021

Status

approved