A378594 First set of a unique partition of the positive integers into two sets whose distinct pair-sums avoid the Lucas numbers.

1, 4, 5, 8, 9, 11, 12, 15, 16, 19, 22, 23, 26, 27, 29, 30, 33, 34, 37, 40, 41, 44, 45, 48, 51, 52, 55, 56, 58, 59, 62, 63, 66, 69, 70, 73, 74, 76, 77, 80, 81, 84, 85, 87, 88, 91, 92, 95, 98, 99, 102, 103, 105, 106, 109, 110, 113, 116, 117, 120, 121, 124, 127

Offset

1,2

Comments

If x, y are distinct elements of this sequence then x+y is not a Lucas number.

Links

Table of n, a(n) for n=1..63.

K. Alladi, P. Erdös, and V. E. Hoggatt, Jr., On additive partitions of integers, Discrete Math. 22 (1978), 201-211.

Crossrefs

Cf. A000032, A378595.

Sequence in context: A042956 A128217 A288671 * A284906 A285260 A375926

Adjacent sequences: A378591 A378592 A378593 * A378595 A378596 A378597

Keyword

nonn

Author

Jeffrey Shallit, Dec 01 2024

Status

approved