A134650 Numbers that are the sum of two consecutive primes (i.e., in A001043) but are not the sum of two sums of two consecutive primes.

5, 8, 12, 18, 52, 100, 946

Offset: 1

Author

N. J. A. Sloane, Jan 25 2008

Keywords

• nonn
• more

Comments

Numbers in A001043 but not in A134651.

Conjectured to be finite, may be complete.

a(8), if it exists, is greater than 20100000. - R. J. Mathar, Jan 26 2008

References

• R. K. Guy, ed., Unsolved Problems, Western Number Theory Meeting, Las Vegas, 1988.

Crossrefs

Cf. A001043, A134651, A135045.

Programs

Maple

with(numtheory): Sset := {}: for i to 15000 do Sset := `union`(Sset, {ithprime(i) + ithprime(i + 1)}) od: Sset := convert(Sset, list): for n from 1 to nops(Sset) do count := 0: s := Sset[n]: for i from 1 to n do if member(s - Sset[i], Sset) and s-Sset[i] >= s/2 then count := count + 1 fi; od: if count = 0 then printf(`%d,`, Sset[n]) fi; od: # James Sellers, Jan 28 2008

Extensions

946 found by James Sellers, Jan 25 2008