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%I #12 Jul 22 2017 08:33:14
%S 5,8,12,18,52,100,946
%N Numbers n such that n is the sum of two consecutive primes (i.e., in A001043) but is not the sum of two sums of two consecutive primes.
%C Numbers in A001043 but not in A134651.
%C Conjectured to be finite, may be complete.
%C a(8), if it exists, is greater than 20100000. - _R. J. Mathar_, Jan 26 2008
%D R. K. Guy, ed., Unsolved Problems, Western Number Theory Meeting, Las Vegas, 1988.
%p 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 A. Sellers_, Jan 28 2008
%Y Cf. A001043, A134651, A135045.
%K nonn,more
%O 1,1
%A _N. J. A. Sloane_, Jan 25 2008
%E 946 found by _James A. Sellers_, Jan 25 2008
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