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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.
2
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.
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
Sequence in context: A324925 A163946 A240500 * A308512 A308857 A244480
KEYWORD
nonn
AUTHOR
Rémy Sigrist, May 13 2021
STATUS
approved