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 A063644 #48 Feb 19 2024 10:33:45
%S A063644 19,29,43,67,173,283,317,653,787,907,1867,2083,2693,2803,3413,3643,
%T A063644 3677,4253,4363,4723,5443,5717,6197,6547,6653,8563,8573,9067,9187,
%U A063644 9403,9643,10733,11443,11587,12163,12917,13997,14107,14683,15187,17827
%N A063644 Primes with 2 representations: p*q*r - 1 = u*v*w + 1 where p, q, r, u, v and w are primes.
%C A063644 Also, primes sandwiched by 3-almost primes. Primes p such that p-+1 are 3-almost primes (A014612). - _Zak Seidov_, Jul 06 2015
%H A063644 Robert G. Wilson v, <a href="/A063644/b063644.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harry J. Smith)
%e A063644 4723 is a term because 4723 = A063639(168)= 4724 - 1 = 2*2*1181 - 1, and because 4723 = A063640(158)= 4722 + 1 = 2*3*787 + 1.
%t A063644 Select[Prime[Range[3000]], 3 == PrimeOmega[# - 1] == PrimeOmega[# + 1] &] (* _Vincenzo Librandi_, Jul 07 2015 *)
%o A063644 (PARI) n=0; default(primelimit, 2000000); for (m=2, 10^9, p=prime(m); if (bigomega(p + 1) == 3 && bigomega(p - 1) == 3, write("b063644.txt", n++, " ", p); if (n==1000, break)) ) \\ _Harry J. Smith_, Aug 27 2009
%o A063644 (PARI) list(lim)=my(v=List(),u=v,L=(lim+1)\2,t); forprime(p=2,L\2, forprime(q=2,min(p,L\p), listput(u,p*q))); u=Set(u); for(i=2,#u, if(u[i]-u[i-1]==1 && isprime(t=2*u[i]-1), listput(v,t))); Vec(v) \\ _Charles R Greathouse IV_, Jan 31 2017
%Y A063644 Cf. A063639, A063640, A014612.
%K A063644 nonn
%O A063644 1,1
%A A063644 _Reinhard Zumkeller_, Jul 21 2001