%I #13 Mar 10 2023 02:21:08
%S 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,
%T 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,
%U 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
%N a(n) = n - 2*b(b(n)) for n >= 2, where b(n) = A356988(n).
%C a(n+1) - a(n) is equal to 1 or -1.
%C 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).
%C a(n) = the distance to the nearest number of the form 2*Fibonacci(k). Cf. A053646.
%H Peter Bala, <a href="/A357562/a357562.pdf">Notes on A357562</a>
%F For k >= 2 there holds
%F a(2*Fibonacci(k) + j ) = j for 0 <= j <= Fibonacci(k-1) and
%F a(Fibonacci(k+2) + j) = Fibonacci(k-1) - j for 0 <= j <= Fibonacci(k-1).
%p # b(n) = A356988(n)
%p b := proc(n) option remember; if n = 1 then 1 else n - b(b(n - b(b(b(n-1))))) end if; end proc:
%p seq( n - 2*b(b(n)), n = 2..100);
%Y Cf. A000045, A053646, A356988, A357563, A357564.
%K nonn,easy
%O 2,7
%A _Peter Bala_, Oct 14 2022