

A166081


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


7



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
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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] (* JeanFrançois Alcover, Mar 24 2020 *)


CROSSREFS

Cf. A000027, A000040, A006881, A038609 (complement), A014092.
Cf. A066615.  R. J. Mathar, Oct 14 2009
Sequence in context: A342334 A066615 A133951 * A111124 A295681 A117308
Adjacent sequences: A166078 A166079 A166080 * A166082 A166083 A166084


KEYWORD

nonn


AUTHOR

JuriStepan Gerasimov, Oct 06 2009


STATUS

approved



