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A118081
Even numbers that can't be represented as the sum of two odd composite numbers.
7
2, 4, 6, 8, 10, 12, 14, 16, 20, 22, 26, 28, 32, 38
OFFSET
1,1
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
EXAMPLE
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.
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 *)
CROSSREFS
Sequence in context: A322405 A360015 A363488 * A152483 A330688 A280743
KEYWORD
fini,full,nonn
AUTHOR
Graeme McRae, Apr 11 2006
STATUS
approved