A287820 - OEIS

%I #30 May 05 2024 19:22:17

%S 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,

%T 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,

%U 2,2,2,5,3,3,3,3,3,3,3,4,3,4,1,4,4,5,4,4

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

%C 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.

%H David A. Corneth, <a href="/A287820/b287820.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%e 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.

%e 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.

%Y Cf. A065108, A261769, A287821.

%K nonn,easy,look

%O 1,4

%A _David A. Corneth_, Jun 01 2017

%E Name clarified by _Chai Wah Wu_, Jun 02 2017