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A110673
Numbers that are neither the sum nor the difference of two primes.
2
23, 37, 47, 53, 67, 79, 83, 89, 93, 97, 113, 117, 119, 121, 123, 127, 131, 143, 145, 157, 163, 167, 173, 185, 187, 203, 205, 207, 211, 215, 217, 219, 223, 233, 245, 247, 251, 257, 263, 277, 287, 289, 293, 297, 299, 301, 303, 307, 317, 321, 323, 325, 327, 331
OFFSET
1,1
COMMENTS
The sequence is obtained by interleaving A099019 and A134797. From Goldbach's conjecture, apparently all terms are odd. - Bob Selcoe, Mar 10 2015
Intersection of A007921 and A014092. - Michel Marcus, Mar 16 2015
LINKS
Oliver Knill, Goldbach for Gaussian, Hurwitz, Octavian and Eisenstein primes, arXiv preprint arXiv:1606.05958 [math.NT], 2016.
MATHEMATICA
Lim=331; nn=PrimePi[Lim+1]; (* Lim is upper limit of sequence; nn is range of primes to consider *)
dif=Union[Flatten[Differences/@Subsets[Prime[Range[nn]], {2}]]]; (* differences of two primes *)
sum=Union[Join[Flatten[Total/@Subsets[Prime[Range[nn]], {2}]], Table[2*Prime[n], {n, nn}]]]; seq2; (* sums of two primes *)
Complement[Range[Lim], dif, sum] (* neither sum nor difference *) (* James C. McMahon, Jun 10 2024 *)
CROSSREFS
Cf. A007921 (not the difference), A014092 (not the sum).
Cf. also A099019, A134797.
Sequence in context: A059798 A290767 A173829 * A134797 A209617 A179780
KEYWORD
easy,nonn
AUTHOR
Eric Angelini, Sep 14 2005
EXTENSIONS
Corrected and extended by Joshua Zucker, May 04 2006
Offset corrected by Arkadiusz Wesolowski, May 19 2012
STATUS
approved