A383430 a(n) is the size of the largest subset of {1,...,n} such that no two elements differ by 5 or 8.

1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 8, 8, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 14, 14, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 20, 20, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 26, 26, 27, 28, 28, 28, 29, 29, 29, 30, 30, 30, 31, 32, 32, 33, 34, 34, 34, 35, 35, 35, 36

Offset: 1

Author

Andrej Jakobcic, May 05 2025

Keywords

• nonn
• easy

Examples

			a(13) = 6 because {1, 2, 4, 5, 8, 11} is a 6-element subset of {1..13} which has no two elements differing by 5 or 8, and there is no larger subset that works.
		

Links

• Mathematics Stack Exchange, Find the maximum number of elements in the set M such that no two elements have a difference of 5 or 8
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,1,-1).

Crossrefs

Cf. A369149.

Programs

Python

def a(n):
    low = [0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 8, 8, 9, 10, 10, 10]
    if n < len(low):
        return low[n]
    else:
        return a(n - 13) + 6

Formula

a(n) = a(n-13) + 6 for n > 20.