A272589 Numbers n such that the equation F(n) = sigma(F(i) + F(j)) has a solution with i >= 1 and j >= 0, where F(k) = A000045(k) represents the k-th Fibonacci number.

1, 2, 4, 6, 7, 12, 24

Offset: 1

Author

Altug Alkan, May 03 2016

Keywords

• nonn
• more

Comments

Corresponding distinct F(n) values for listed terms are 1, 3, 8, 13, 144, 46368.

Corresponding F(i) + F(j) values are for listed terms are 1, 2, 7, 9, 94, 28678.

It is known that for almost all positive integers n, the sum of divisors of Fibonacci(n) is not a Fibonacci number (see A272412). This sequence focuses on the sums of two Fibonacci numbers for a similar question. Since A000045 is obvious subsequence of A084176 by definition of Fibonacci numbers, the reason of existence of this sequence can be seen as a generalized version of question that is motivation of A272412.

Examples

			7 is a term because Fibonacci(7) = 13 = sigma(1 + 8) and 1, 8 are Fibonacci numbers.
		

Crossrefs

Cf. A000203, A000045, A084176, A272412.