A166081 - OEIS

%I #36 Apr 18 2023 09:44:00

%S 1,2,3,4,6,11,17,23,27,29,35,37,41,47,51,53,57,59,65,67,71,77,79,83,

%T 87,89,93,95,97,101,107,113,117,119,121,123,125,127,131,135,137,143,

%U 145,147,149,155,157,161,163,167,171,173,177,179,185,187,189,191,197,203

%N Natural numbers that are not the sum of two distinct primes.

%C All numbers that appear in A014092 are also in this sequence, by definition.

%C It seems that, for n > 6, the reverse is also true, however this is unproved. - _Ely Golden_, Dec 25 2016

%C All numbers that appear in this sequence but not A014092 must be even semiprimes with no other partitions into primes. - _Ely Golden_, Dec 25 2016

%H Alois P. Heinz, <a href="/A166081/b166081.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from G. C. Greubel)

%F {1} U A025584 U A109934. - _R. J. Mathar_, Oct 08 2009

%F A000027 \ A038609. - _R. J. Mathar_, Oct 14 2009

%t Select[Range@ 204, Length@Select[Transpose@{#, Reverse@ # - 1} &@ Range[#] &@ #, Times @@ Boole@ Map[PrimeQ, #] == 1 && First@ # != Last@ # &] == 0 &] (* _Michael De Vlieger_, Apr 24 2016 *)

%t max = 1000;

%t ip = PrimePi[max];

%t A038609 = Table[Prime[i] + Prime[j], {i, ip}, {j, i + 1, ip}] // Flatten // Union // Select[#, # <= max&]&;

%t Complement[Range[max], A038609] (* _Jean-François Alcover_, Mar 24 2020 *)

%Y Cf. A117929, A006881, A038609 (complement), A014092, A066615.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Oct 06 2009