A118081 Even numbers that can't be represented as the sum of two odd composite numbers.

2, 4, 6, 8, 10, 12, 14, 16, 20, 22, 26, 28, 32, 38

Offset: 1

Author

Graeme McRae, Apr 11 2006

Keywords

• fini
• full
• nonn

Comments

Suggested by the familiar puzzle, "What is the largest even number that is not the sum of two odd composite numbers?" The sequence contains all even numbers that are not of the form (9+6k)+9, (9+6k)+25, or (9+6k)+35, where k is a nonnegative integer.

If 1 is allowed as a composite number, then only the eight numbers in A046458 are not representable. - T. D. Noe, Jun 01 2008

Examples

			38 is in the sequence because 38 == 2 (mod 3) and all even numbers congruent to 2 mod 3 larger than 38 can be expressed as the sum of odd composites (9+6k) and 35, where k is a nonnegative integer.
		

Programs

Mathematica

ocn=Select[Range[3,37,2],!PrimeQ[#]&];s=Total/@Tuples[ocn,2];Complement[Range[2,38,2],s] (* James C. McMahon, Sep 23 2024 *)