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A166081
Natural numbers that are not the sum of two distinct primes.
10
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
KEYWORD
nonn
AUTHOR
STATUS
approved