This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A157995 #13 Sep 01 2025 01:03:43
%S A157995 19,31,43,53,79,101,113,139,163,173,199,211,223,241,269,331,353,373,
%T A157995 463,509,521,577,601,619,631,727,773,787,811,829,853,883,907,919,947,
%U A157995 967,991,1013,1031,1181,1193,1231,1291,1301,1361,1429,1447,1483,1531,1543
%N A157995 Primes which are the sum of 1 plus two consecutive not-twin primes, p1 and p2, (p2-p1)>2.
%H A157995 Robert Israel, <a href="/A157995/b157995.txt">Table of n, a(n) for n = 1..10000</a>
%e A157995 19=7+11+1, 31=13+17+1, 43=19+23+1, 53=23+29+1, 79=37+41+1, 101=47+53+1, ...
%p A157995 count:= 0: R:= NULL: p:= 2:
%p A157995 while count < 100 do
%p A157995 q:= p; p:= nextprime(p);
%p A157995 if p-q > 2 and isprime(p+q+1) then
%p A157995 count:= count+1; R:= R, p+q+1
%p A157995 fi
%p A157995 od:
%p A157995 R; # _Robert Israel_, May 13 2020
%t A157995 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
%t A157995 Select[Total[#]+1&/@Select[Partition[Prime[Range[200]],2,1],Last[#]-First[#]>2&],PrimeQ] (* _Harvey P. Dale_, Mar 13 2011 *)
%Y A157995 Cf. A005385, A092738, A118071.
%K A157995 nonn,changed
%O A157995 1,1
%A A157995 _Vladimir Joseph Stephan Orlovsky_, Mar 11 2009
%E A157995 Definition corrected by _Harvey P. Dale_, Mar 13 2011