A157995 Primes which are the sum of 1 plus two consecutive not-twin primes, p1 and p2, (p2-p1)>2.

19, 31, 43, 53, 79, 101, 113, 139, 163, 173, 199, 211, 223, 241, 269, 331, 353, 373, 463, 509, 521, 577, 601, 619, 631, 727, 773, 787, 811, 829, 853, 883, 907, 919, 947, 967, 991, 1013, 1031, 1181, 1193, 1231, 1291, 1301, 1361, 1429, 1447, 1483, 1531, 1543

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Mar 11 2009

Keywords

• nonn
• changed

Examples

			19=7+11+1, 31=13+17+1, 43=19+23+1, 53=23+29+1, 79=37+41+1, 101=47+53+1, ...
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005385, A092738, A118071.

Programs

Maple

count:= 0: R:= NULL: p:= 2:
while count < 100 do
  q:= p; p:= nextprime(p);
  if p-q > 2 and isprime(p+q+1) then
     count:= count+1; R:= R, p+q+1
  fi
od:
R; # Robert Israel, May 13 2020

Mathematica

lst={};Do[p0=Prime[n];p1=Prime[n+1];a=p0+p1+1;If[PrimeQ[a]&&(p1-p0)>2,AppendTo[lst,a]],{n,6!}];lst
Select[Total[#]+1&/@Select[Partition[Prime[Range[200]],2,1],Last[#]-First[#]>2&],PrimeQ]  (* Harvey P. Dale, Mar 13 2011 *)

Extensions

Definition corrected by Harvey P. Dale, Mar 13 2011