A166081 Natural numbers that are not the sum of two distinct primes.

1, 2, 3, 4, 6, 11, 17, 23, 27, 29, 35, 37, 41, 47, 51, 53, 57, 59, 65, 67, 71, 77, 79, 83, 87, 89, 93, 95, 97, 101, 107, 113, 117, 119, 121, 123, 125, 127, 131, 135, 137, 143, 145, 147, 149, 155, 157, 161, 163, 167, 171, 173, 177, 179, 185, 187, 189, 191, 197, 203

Offset

1,2

Comments

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

It seems that, for n > 6, the reverse is also true, however this is unproved. - Ely Golden, Dec 25 2016

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from G. C. Greubel)

Formula

{1} U A025584 U A109934. - R. J. Mathar, Oct 08 2009

A000027 \ A038609. - R. J. Mathar, Oct 14 2009

Mathematica

Select[Range@ 204, Length@Select[Transpose@{#, Reverse@ # - 1} &@ Range[#] &@ #, Times @@ Boole@ Map[PrimeQ, #] == 1 && First@ # != Last@ # &] == 0 &] (* Michael De Vlieger, Apr 24 2016 *)
max = 1000;
ip = PrimePi[max];
A038609 = Table[Prime[i] + Prime[j], {i, ip}, {j, i + 1, ip}] // Flatten // Union // Select[#, # <= max&]&;
Complement[Range[max], A038609] (* Jean-François Alcover, Mar 24 2020 *)

Crossrefs

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

Sequence in context: A342334 A066615 A133951 * A111124 A295681 A117308

Adjacent sequences: A166078 A166079 A166080 * A166082 A166083 A166084

Keyword

nonn

Author

Juri-Stepan Gerasimov, Oct 06 2009

Status

approved