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A374318
For any n > 0, let b_n(n+1) = 0, and for k = 1..n, if b_n(k+1) >= k then b_n(k) = b_n(k+1) - k otherwise b_n(k) = b_n(k+1) + k; a(n) = b_n(1).
2
0, 1, 1, 0, 2, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1
OFFSET
0,5
COMMENTS
This sequence is a variant of A008344; here we add or subtract by numbers from n down to 1, there by numbers from 1 up to n.
Apparently, the sequence only contains 0's, 1's and 2's.
FORMULA
Empirically, a(n) = 1 iff n belongs to A042963.
EXAMPLE
The first terms, alongside the corresponding sequences b_n, are:
n a(n) b_n
-- ---- ----------------------------------
0 0 [0]
1 1 [1, 0]
2 1 [1, 2, 0]
3 0 [0, 1, 3, 0]
4 2 [2, 3, 1, 4, 0]
5 1 [1, 2, 4, 1, 5, 0]
6 1 [1, 0, 2, 5, 1, 6, 0]
7 2 [2, 3, 5, 2, 6, 1, 7, 0]
8 0 [0, 1, 3, 6, 2, 7, 1, 8, 0]
9 1 [1, 2, 0, 3, 7, 2, 8, 1, 9, 0]
10 1 [1, 2, 4, 7, 3, 8, 2, 9, 1, 10, 0]
PROG
(PARI) a(n) = { my (b = 0); forstep (k = n, 1, -1, if (b >= k, b -= k, b += k); ); return (b); }
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jul 04 2024
STATUS
approved