A357564 -id:A357564 - cp's OEIS frontend

A357562 a(n) = n - 2*b(b(n)) for n >= 2, where b(n) = A356988(n).

0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12

Offset: 2

Peter Bala, Oct 14 2022

a(n+1) - a(n) is equal to 1 or -1.
The sequence vanishes at abscissa values n = 2, 4, 6, 10, 16, 26, ..., 2*Fibonacci(k), .... For k >= 2, the line graph of the sequence, starting from the zero value at abscissa n = 2*Fibonacci(k), ascends with slope 1 to a local peak at height Fibonacci(k-1) at abscissa value n = Fibonacci(k+2) before descending with slope -1 to the next zero at abscissa n = 2*Fibonacci(k+1).
a(n) = the distance to the nearest number of the form 2*Fibonacci(k). Cf. A053646.

Peter Bala, Notes on A357562

Cf. A000045, A053646, A356988, A357563, A357564.

# b(n) = A356988(n)
b := proc(n) option remember; if n = 1 then 1 else n - b(b(n - b(b(b(n-1))))) end if; end proc:
seq( n - 2*b(b(n)), n = 2..100);

For k >= 2 there holds
a(2*Fibonacci(k) + j ) = j for 0 <= j <= Fibonacci(k-1) and
a(Fibonacci(k+2) + j) = Fibonacci(k-1) - j for 0 <= j <= Fibonacci(k-1).

cp's OEIS Frontend

A357562 a(n) = n - 2*b(b(n)) for n >= 2, where b(n) = A356988(n).

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