A378595 Second set of a unique partition of the positive integers into two sets whose distinct pair-sums avoid the Lucas numbers.

2, 3, 6, 7, 10, 13, 14, 17, 18, 20, 21, 24, 25, 28, 31, 32, 35, 36, 38, 39, 42, 43, 46, 47, 49, 50, 53, 54, 57, 60, 61, 64, 65, 67, 68, 71, 72, 75, 78, 79, 82, 83, 86, 89, 90, 93, 94, 96, 97, 100, 101, 104, 107, 108, 111, 112, 114, 115, 118, 119, 122, 123, 125

Offset

1,1

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, A378594.

Sequence in context: A330572 A287241 A331075 * A062720 A069813 A266534

Adjacent sequences: A378592 A378593 A378594 * A378596 A378597 A378598

Keyword

nonn,new

Author

Jeffrey Shallit, Dec 01 2024

Status

approved