A398227

Nonnegative numbers that are not the sum of two Lucas numbers.

Created: 8/6/2026 | Author: Vincenzo Manto , Jul 24 2026

This sequence has been cited by and influenced 1 other sequence

Official Comments

The sequence of Lucas numbers used is A000032 (including 2).
The sequence excludes the sum of two Lucas numbers, even if they are equal.
It differs from A054770 by including 2 as a valid addend and the sum of two identical Lucas numbers (A000032(i) + A000032(i)) is also allowed. Therefore, numbers formed by those valid additions are excluded from this sequence.
The sequence tends to become denser for high n, due to the decreasing density of Lucas numbers.

Sequence Chart

Data

0,1,16,17,23,24,26,27,28,34,35,37,38,39,41,42,43,44,45,46,52,53,55,56,57,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,81,82,84,85,86,88,89,90,91,92,93,95,96,97,98,99,100,101,102,103,104,106,107,108,109

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(105) if n not in sums])

Mathematica

ln=LucasL[Range[0, 10]];Complement[Range[0,Max[ln]],Select[Total/@Tuples[ln,2],#<Max[ln]&]] (* _James C. McMahon_, Aug 07 2026 *)

Cross-References

See also OEIS entries: Cf A054770 A059390 A000032