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).

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

Links

Table of n, a(n) for n=1..87.

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

Cf. A002275, A005206, A005614, A285431, A286389, A368282.

Sequence in context: A275694 A267922 A267358 * A153860 A254377 A285657

Adjacent sequences: A368278 A368279 A368280 * A368282 A368283 A368284

Keyword

nonn,tabl

Author

Chai Wah Wu, Dec 19 2023

Status

approved