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 A307533 #82 Jul 29 2019 04:33:46 %S A307533 13,19,31,37,43,53,61,67,73,83,89,97,109,113,127,131,139,151,157,173, %T A307533 181,199,211,223,233,251,257,263,277,293,307,317,331,337,349,353,367, %U A307533 373,379,389,401,409,421,439,443,449,457,467,479,487,491,499,503,509,541 %N A307533 Primes p such that p+2 has exactly two distinct prime factors. %C A307533 (13,31), (37,73), (157,751), (199,991) are pairs of emirps belonging to this sequence such that the lesser term of the pair is the reverse of the greater. Are there infinitely many such pairs? %C A307533 Are there infinitely many triples in the sequence like (61,67,73) and (251,257,263), that is, infinitely many a(n) such that a(n+1)=a(n)+6 and a(n+2)=a(n)+12? %C A307533 The triples found so far are (61,67,73), (251,257,263) and (367,373,379). The first terms of the triples found are 61, 251 and 367, which belong to the sequence A038107. %H A307533 Robert Israel, <a href="/A307533/b307533.txt">Table of n, a(n) for n = 1..10000</a> %e A307533 61 is in the sequence because 61 + 2 = 63 has exactly two distinct prime factors (3 and 7). %p A307533 filter:= proc(n) isprime(n) and nops(numtheory:-factorset(n+2))=2 end proc: %p A307533 select(filter, [seq(i,i=3..1000,2)]); # _Robert Israel_, Jul 28 2019 %t A307533 Select[Range[500], PrimeQ[#] && PrimeNu[# + 2] == 2 &] (* _Amiram Eldar_, Apr 14 2019 *) %o A307533 (PARI) isok(p) = isprime(p) && (omega(p+2) == 2); \\ _Michel Marcus_, May 02 2019 %K A307533 nonn,less %O A307533 1,1 %A A307533 _Paolo Galliani_, Apr 13 2019