A104857 Positive integers that cannot be represented as the sum of distinct Lucas 3-step numbers (A001644).

2, 5, 6, 9, 13, 16, 17, 20, 23, 26, 27, 30, 34, 37, 38, 41, 44, 45, 48, 52, 55, 56, 59, 62, 65, 66, 69, 73, 76, 77, 80, 84, 87, 88, 91, 94, 97, 98, 101, 105, 108, 109, 112, 115, 116, 119, 123, 126, 127, 130, 133, 136, 137, 140, 144, 147, 148, 151, 154

Offset: 1

Author

Jonathan Vos Post, Apr 24 2005

Keywords

• easy
• nonn

Comments

Similar to A054770 "Numbers that are not the sum of distinct Lucas numbers (A000204)" but with Lucas 3-step numbers (A001644). Wanted: equivalent of David W. Wilson conjecture (A054770) as proved by Ian Agol. Note that all positive integers can be presented as the sum of distinct Fibonacci numbers in A000119 way. Catalani called Lucas 3-step numbers "generalized Lucas numbers" but that is quite ambiguous. These are also called tribonacci-Lucas numbers.

Examples

			In "base Lucas 3-step numbers" we can represent 1 as "1", but cannot represent 2 because there is no next Lucas 3-step number until 3 and we can't have two instances of 1 summed here. We can represent 3 as "10" (one 3 and no 1's), 4 as "11" (one 3 and one 1). Then we cannot represent 5 or 6 because there is no next Lucas 3-step number until 7 and we can't sum two 3s or six 1's. 7 becomes "100" (one 7, no 3s and no 1's), 8 becomes "101" and so forth.
		

Links

• Eric Weisstein's World of Mathematics, Lucas n-Step Number.

Crossrefs

Cf. A000119, A001644, A054770.

Extensions

More terms from T. D. Noe, Apr 26 2005