A398228
Numbers that are the sum of two Lucas numbers.
Official Comments
The sequence of Lucas numbers used is A000032 (including 2).
The sequence includes the sum of two Lucas numbers, even if they are equal.
The sequence tends to become less dense for large values of n, due to the decreasing density of Lucas numbers.
It differs from A063732 by including 2 as a valid addend and the sum of two identical Lucas numbers (A000032(i) + A000032(i)) is also allowed, but A063732 includes sums of more than two Lucas numbers.
Sequence Chart
Data
2,3,4,5,6,7,8,9,10,11,12,13,14,15,18,19,20,21,22,25,29,30,31,32,33,36,40,47,48,49,50,51,54,58,65,76,77,78,79,80,83,87,94,105,123,124,125,126,127,130,134,141,152,170,199,200,201,202,203,206,210,217,228,246,275
Computational Implementations
PYTHON
from sympy import lucas
from itertools import combinations_with_replacement
lucas_seq = [lucas(i) for i in range(30)]
sums = {a + b for a, b in combinations_with_replacement(lucas_seq, 2)}
print([n for n in range(300) if n in sums])Mathematica
L=LucasL[Range[0,12]];Select[Union[Total/@Tuples[L,2]],#<=Max[L]+1&] (* _James C. McMahon_, Aug 21 2026 *)Cross-References
See also OEIS entries: Cf A054770 A059389 A000032 A063732, Complement of A398227