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 A059322 #36 Mar 02 2025 16:03:51
%S A059322 2,4,12,24,12,24,24,60,12,48,36,84,12,24,84,12,24,60,24,132,120,24,24,
%T A059322 96,36,168,96,24,12,48,72,48,36,96,204,84,120,12,24,36,108,240,12,120,
%U A059322 240,60,24,60,36,24,96,48,36,264,156,156,24,60,84,60,72,48,12,120,24
%N A059322 First differences of sequence of consecutive safe primes.
%C A059322 Except for (5,7) and (7,11), all terms are divisible by 12, since safe primes are congruent to 5 modulo 6 except 7 and safe_prime + 6 is not a safe prime. Closest safe primes differ by 12 like (11,23) or (83207,83219).
%H A059322 Amiram Eldar, <a href="/A059322/b059322.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..5001 from G. C. Greubel)
%F A059322 a(n) = A005385(n+1) - A005385(n). [corrected by _Harvey P. Dale_, Jan 12 2011 and _Zak Seidov_, Sep 19 2016]
%t A059322 Differences[Select[Prime[Range[500]],PrimeQ[(#-1)/2]&]] (* _Harvey P. Dale_, Jan 12 2011 *)
%o A059322 (PARI) list(lim) = {my(p1 = 5); forprime(p2 = 7, lim, if(isprime((p2-1)/2), print1(p2-p1, ", "); p1 = p2));} \\ _Amiram Eldar_, Mar 02 2025
%Y A059322 Cf. A005385, A033299.
%K A059322 nonn
%O A059322 1,1
%A A059322 _Labos Elemer_, Jan 26 2001
%E A059322 Offset corrected by _Amiram Eldar_, Mar 02 2025