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

0,11

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.

Links

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

Formula

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

Example

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

Prog

(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)

Crossrefs

Cf. A000045, A296239.

Sequence in context: A297964 A296239 A039800 * A251418 A172101 A301365

Adjacent sequences: A309413 A309414 A309415 * A309417 A309418 A309419

Keyword

nonn

Author

Rémy Sigrist, Jul 30 2019

Status

approved