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A166081 Natural numbers that not are the sum of two distinct primes. 6
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 (list; graph; refs; listen; history; text; internal format)
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

G. C. Greubel, Table of n, a(n) for n = 1..1000

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 *)

CROSSREFS

Cf. A000027, A000040, A006881, A014092.

Cf. A066615. - R. J. Mathar, Oct 14 2009

Sequence in context: A116853 A066615 A133951 * A111124 A295681 A117308

Adjacent sequences:  A166078 A166079 A166080 * A166082 A166083 A166084

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Oct 06 2009

STATUS

approved

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Last modified December 10 03:07 EST 2018. Contains 318044 sequences. (Running on oeis4.)