A309416 a(n) = Sum_{k > 0} d^k(n), where d^k corresponds to the k-th iterate of A296239.

0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 2, 2, 1, 0, 1, 2, 3, 5, 3, 2, 1, 0, 1, 2, 3, 5, 5, 7, 7, 5, 5, 3, 2, 1, 0, 1, 2, 3, 5, 5, 7, 8, 8, 10, 12, 12, 10, 8, 8, 7, 5, 5, 3, 2, 1, 0, 1, 2, 3, 5, 5, 7, 8, 8, 10, 12, 13, 13, 13, 15, 17, 19, 22, 19, 17, 15, 13, 13, 13, 12

Offset: 0

Author

Rémy Sigrist, Jul 30 2019

Keywords

• nonn

Comments

Iterating A296239 from any nonnegative number always leads to the fixed point 0, hence the series in the name has only finitely many nonzero terms and is well defined.

Examples

			For n = 1024:
- A296239(1024) = 37,
- A296239(37) = 3,
- A296239(3) = 0,
- hence a(1024) = 37 + 3 = 40.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10946

Crossrefs

Cf. A000045, A296239.

Programs

PARI

A296239(n) = for (i=1, oo, if (n<=fibonacci(i), return (min(n-fibonacci(i-1), fibonacci(i)-n))))
a(n) = my (v=0); while (n=A296239(n), v+=n); return (v)

Formula

a(n) = 0 iff n is a Fibonacci number.