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%I #13 Apr 18 2018 23:45:18
%S 2,5,6,9,13,16,17,20,23,26,27,30,34,37,38,41,44,45,48,52,55,56,59,62,
%T 65,66,69,73,76,77,80,84,87,88,91,94,97,98,101,105,108,109,112,115,
%U 116,119,123,126,127,130,133,136,137,140,144,147,148,151,154
%N Positive integers that cannot be represented as the sum of distinct Lucas 3-step numbers (A001644).
%C 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.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Lucasn-StepNumber.html">Lucas n-Step Number</a>.
%e 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.
%Y Cf. A000119, A001644, A054770.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Apr 24 2005
%E More terms from _T. D. Noe_, Apr 26 2005
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