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A368281
Table T(n,k) n>=1, k>=1, read by downwards antidiagonals where the n-th row is the fixed point of the morphism 0->R(n), 1->R(n)0, where R(n) is the n-th repunit (A002275).
2
1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1
OFFSET
1
FORMULA
First row: A005614.
Second row: A285431.
Conjecture: if a(k) is the fixed point of the morphism 0->R(n), 1->R(n)0, then the partial sum of a(k) is the Hofstadter-like sequence b(k): b(0)=0, b(k) = k - b(floor(b(k-1)/n)), i.e., the partial sum of the n-th row of A368281 is the n-th row of A368282. The cases n=1 and n=2 are known to be true (see A005206, A286389).
EXAMPLE
Table begins:
k
n=1: 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, ...
n=2: 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, ...
n=3: 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, ...
n=4: 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, ...
n=5: 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, ...
n=6: 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, ...
n=7: 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, ...
n=8: 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, ...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Chai Wah Wu, Dec 19 2023
STATUS
approved