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URL: https://oeis.org/A386987

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A386987
For n >= 2, a(n) is the least r >= 1 such that T(n - r) + ... + T(n - 1) = T(n + 1) + ... + T(n + r) where T(i) is A010060(i).
0
2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 4, 3, 3
OFFSET
2,1
COMMENTS
a(n) is from {1, 2, 3, 4}.
FORMULA
a(A081706(n) + 1) = 1.
a(2*A079523(n)) = 2.
a(A249034(n))= 2.
a(A225822(n)) = 3.
a(A056196(n)) = 3.
a(2*A131323(n)) = 4.
a(2*A249034(n) - 1) = 4.
EXAMPLE
For n = 6: T(6 - r) + ... + T(5) = T(7) + ... + T(6 + r) is true for the least r = 4 because A010060(2) + A010060(3) + A010060(4) + A010060(5) = A010060(7) + A010060(8) + A010060(9) + A010060(10), thus a(6) = 4.
MATHEMATICA
a[n_] := Module[{s = 0, r = 1}, While[r <= n && (r == 1 || s != 0), s += (ThueMorse[n - r] - ThueMorse[n + r]); r++]; r-1]; Array[a, 100, 2] (* Amiram Eldar, Aug 12 2025 *)
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, Aug 12 2025
STATUS
approved