

A104857


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


0



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Similar to A054770 "Numbers that are not the sum of distinct Lucas numbers (A000204)" but with Lucas 3step 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 3step numbers "generalized Lucas numbers" but that is quite ambiguous. These are also called tribonacciLucas numbers.


LINKS

Table of n, a(n) for n=1..59.
Eric Weisstein's World of Mathematics, Lucas nStep Number.


EXAMPLE

In "base Lucas 3step numbers" we can represent 1 as "1", but cannot represent 2 because there is no next Lucas 3step 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 3step 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.


CROSSREFS

Cf. A000119, A001644, A054770.
Sequence in context: A219764 A286003 A094350 * A285899 A055198 A103982
Adjacent sequences: A104854 A104855 A104856 * A104858 A104859 A104860


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Apr 24 2005


EXTENSIONS

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


STATUS

approved



