A367499 - OEIS

%I #21 Jan 21 2024 09:18:48

%S 3,5,6,9,11,12,14,16,17,20,22,23,25,26,29,31,34,36,37,40,42,43,46,48,

%T 49,51,53,54,57,60,62,63,66,68,71,73,74,77,79,80,82,84,85,88,90,91,93,

%U 94,97,99,102,104,105,108,110,111,114,116,117,119,121,122,125

%N Lexicographically least increasing sequence of positive integers, beginning with 3, with the property that no sum of two distinct terms is a Tribonacci number.

%C This sequence is the complement of A367498.  In fact, this and A367498 together form the unique partition of the positive integers into two disjoint sets, each having the property that the sum of two distinct elements is never a Tribonacci number.

%H Robert Israel, <a href="/A367499/b367499.txt">Table of n, a(n) for n = 1..10000</a>

%H V. E. Hoggatt, Jr., <a href="https://www.fq.math.ca/Scanned/18-3/hoggatt.pdf">Additive partitions of the positive integers</a>, Fib. Quart. 18 (1980), 220-225.

%p N:= 500: # for terms <= N

%p T:= {0,1}: b:= 0: c:= 1: d:= 1:

%p do

%p   a:= b; b:= c; c:= d; d:= a+b+c;

%p   if d > 2*N then break fi;

%p   T:= T union {d}

%p od:

%p A:= {3}:

%p for i from 4 to N do

%p   Tp:= map(`-`,T,i);

%p   if Tp intersect A = {} then A:= A union {i} fi

%p od:

%p sort(convert(A,list)); # _Robert Israel_, Jan 20 2024

%Y Cf. A000073, A367498.

%K nonn

%O 1,1

%A _Jeffrey Shallit_, Nov 20 2023