A118081 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

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

(list; graph; refs; listen; history; text; internal format)

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

LINKS

Table of n, a(n) for n=1..14.

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

Adjacent sequences: A118078 A118079 A118080 * A118082 A118083 A118084

KEYWORD

fini,full,nonn,changed

AUTHOR

Graeme McRae, Apr 11 2006

STATUS

approved