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A367499
Lexicographically least increasing sequence of positive integers, beginning with 3, with the property that no sum of two distinct terms is a Tribonacci number.
2
3, 5, 6, 9, 11, 12, 14, 16, 17, 20, 22, 23, 25, 26, 29, 31, 34, 36, 37, 40, 42, 43, 46, 48, 49, 51, 53, 54, 57, 60, 62, 63, 66, 68, 71, 73, 74, 77, 79, 80, 82, 84, 85, 88, 90, 91, 93, 94, 97, 99, 102, 104, 105, 108, 110, 111, 114, 116, 117, 119, 121, 122, 125
OFFSET
1,1
COMMENTS
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.
LINKS
V. E. Hoggatt, Jr., Additive partitions of the positive integers, Fib. Quart. 18 (1980), 220-225.
MAPLE
N:= 500: # for terms <= N
T:= {0, 1}: b:= 0: c:= 1: d:= 1:
do
a:= b; b:= c; c:= d; d:= a+b+c;
if d > 2*N then break fi;
T:= T union {d}
od:
A:= {3}:
for i from 4 to N do
Tp:= map(`-`, T, i);
if Tp intersect A = {} then A:= A union {i} fi
od:
sort(convert(A, list)); # Robert Israel, Jan 20 2024
CROSSREFS
Sequence in context: A122194 A225005 A053091 * A324701 A047271 A047445
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Nov 20 2023
STATUS
approved