A099019 -id:A099019 - cp's OEIS frontend

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

Eric Angelini, Sep 14 2005

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

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

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

Cf. also A099019, A134797.

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 *)

Corrected and extended by Joshua Zucker, May 04 2006

Offset corrected by Arkadiusz Wesolowski, May 19 2012

A129822 Array read by rows: each row lists three consecutive nonprime odd numbers.

Original entry on oeis.org

91, 93, 95, 115, 117, 119, 117, 119, 121, 119, 121, 123, 121, 123, 125, 141, 143, 145, 143, 145, 147, 183, 185, 187, 185, 187, 189, 201, 203, 205, 203, 205, 207, 205, 207, 209, 213, 215, 217, 215, 217, 219, 217, 219, 221, 243, 245, 247, 245, 247, 249, 285

Offset: 1

Roger L. Bagula, May 20 2007

Robert Israel, Table of n, a(n) for n = 1..10002

Cf. A099019 (second column), A161945 (first column).

a:=proc(n) if isprime(2*n-1)=false and isprime(2*n+1)=false and isprime(2*n+3)=false then 2*n-1, 2*n+1, 2*n+3 else fi end: seq(a(n),n=1..150);

Flatten[Table[If[OddQ[n - 1] && PrimeQ[n - 1] == False && PrimeQ[n + 1] == False && PrimeQ[n + 3] == False, {{n - 1}, {n + 1}, {n + 3}}, {}], {n, 2, 300}]]
Select[Partition[Range[1,301,2],3,1],NoneTrue[#,PrimeQ]&]//Flatten (* Harvey P. Dale, Jul 16 2021 *)

Edited by N. J. A. Sloane, Jun 09 2007

Definition modified by Harvey P. Dale, Jul 16 2021

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions