A357562 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,7

COMMENTS

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.

LINKS

Table of n, a(n) for n=2..98.

Peter Bala, Notes on A357562

FORMULA

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).

MAPLE

# 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);