A357589 a(n) = n - A130312(n).

0, 1, 1, 2, 2, 3, 4, 3, 4, 5, 6, 7, 5, 6, 7, 8, 9, 10, 11, 12, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36

Offset: 1

Author

Mikhail Kurkov, Oct 05 2022

Keywords

• nonn
• easy

Crossrefs

Cf. A130312, A183544.

Programs

PARI

b1(n)=local(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2) \\ A072649
a(n)=n - fibonacci(b1(n))

Python

from itertools import islice
def A357589_gen(): # generator of terms
    a, b, i = 1, 1, 1
    while True:
        yield from (j-a for j in range(i,i+a))
        i += a
        a, b = b, a+b
A357589_list = list(islice(A357589_gen(),30)) # Chai Wah Wu, Oct 13 2022

Formula

Conjecture: a(n) = 2*n - 1 - A183544(n).