A046458 -id:A046458 - cp's OEIS frontend

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

Graeme McRae, Apr 11 2006

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

			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.

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

A141099 Number of unordered pairs of odd nonprime numbers that sum to 2n.

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 0, 2, 3, 0, 2, 3, 1, 2, 3, 3, 2, 4, 2, 3, 5, 1, 4, 6, 1, 5, 5, 3, 4, 7, 3, 4, 7, 4, 4, 9, 4, 5, 8, 4, 7, 9, 5, 6, 8, 6, 7, 10, 6, 6, 13, 5, 7, 13, 5, 10, 11, 8, 8, 11, 9, 10, 14, 9, 9, 16, 7, 12, 15, 8, 12, 15, 9, 10, 17, 14, 11, 16, 12, 12, 19, 11, 13, 19

Offset: 1

T. D. Noe, Jun 02 2008, Jun 05 2008

nonn

See A141100 for pairs of odd composite numbers. We have a(n) > 0 except for the 8 values of 2n given in A046458.

			a(18)=3 because 36 = 1+35 = 9+27 = 15+21.

T. D. Noe, Table of n, a(n) for n=1..1000

Cf. A141095, A141097.

Table[cnt=0; Do[If[ !PrimeQ[i] && !PrimeQ[2n-i], cnt++ ], {i,1,n,2}]; cnt, {n,100}]

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Programs

Mathematica