A309416 - OEIS

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

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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

R�my 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))))