A110673 Numbers that are neither the sum nor the difference of two primes.

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

Author

Eric Angelini, Sep 14 2005

Keywords

• easy
• nonn

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

• Michel Marcus, Table of n, a(n) for n = 1..7596
• Oliver Knill, Goldbach for Gaussian, Hurwitz, Octavian and Eisenstein primes, arXiv preprint arXiv:1606.05958 [math.NT], 2016.
• Wikipedia, Goldbach's conjecture

Crossrefs

Cf. A007921 (not the difference), A014092 (not the sum).

Cf. also A099019, A134797.

Programs

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 *)

Extensions

Corrected and extended by Joshua Zucker, May 04 2006

Offset corrected by Arkadiusz Wesolowski, May 19 2012