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.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A000073, A367498.

Sequence in context: A122194 A225005 A053091 * A324701 A047271 A047445

Adjacent sequences: A367496 A367497 A367498 * A367500 A367501 A367502

Keyword

nonn

Author

Jeffrey Shallit, Nov 20 2023

Status

approved