A287820 Least number of factors to express A065108(n) as a product of Fibonacci numbers.

0, 1, 1, 2, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 3, 1, 2, 2, 2, 3, 3, 3, 1, 4, 2, 2, 2, 3, 3, 3, 3, 4, 1, 4, 2, 2, 2, 2, 3, 3, 3, 3, 4, 3, 1, 4, 4, 4, 2, 2, 2, 5, 2, 3, 3, 3, 3, 3, 3, 4, 3, 1, 4, 4, 4, 5, 2, 2, 2, 2, 2, 5, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 1, 4, 4, 5, 4, 4

Offset

1,4

Comments

Some terms of A065108 are a product of Fibonacci numbers in more than one way. For example, 8 is a product of Fibonacci numbers in more than one way as 8 = 2 * 2 * 2 and both 8 and 2 are Fibonacci numbers. Therefore, 'at least' is used in the name.

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

8 = 2 * 2 * 2 are all ways to write A065108(7) = 8 as a product of Fibonacci numbers. 8 has one factor, the least number of all such factorizations. Therefore, a(7) = 1.
81 = 3^4. 81 isn't a Fibonacci number. 3^4 is the only factorization of A065108(43) = 81 into Fibonacci numbers and has four factors 3. Therefore, a(43) = 4.
144 = 2 * 3 * 3 * 8 = 2 * 2 * 2 * 2 * 3 * 3 are all ways to write A065108(62) = 144 as a product of fibonacci numbers. 144 has one factor, the least number of all such factorizations. Therefore, a(62) = 1.

Crossrefs

Cf. A065108, A261769, A287821.

Sequence in context: A308964 A124830 A291598 * A191373 A322873 A332897

Adjacent sequences: A287817 A287818 A287819 * A287821 A287822 A287823

Keyword

nonn,easy,look

Author

David A. Corneth, Jun 01 2017

Extensions

Name clarified by Chai Wah Wu, Jun 02 2017

Status

approved