A059395 - OEIS

%I #12 Jan 13 2020 09:33:05

%S 467,1307,2447,5087,5927,12527,18947,44687,78467,83207,118787,143687,

%T 164987,196907,204587,207227,208787,229487,236507,257627,275987,

%U 297707,330887,339827,367007,369647,394007,454907,458807,474347,534827,536087

%N Smaller of safe prime twins: special safe primes (A005385) p such that the next prime is also the next safe prime and is p+12, i.e., occurs at the closest possible distance, 12.

%H Amiram Eldar, <a href="/A059395/b059395.txt">Table of n, a(n) for n = 1..10000</a>

%e The pairs (5,7) and (7,11) are omitted, albeit are both consecutive primes and consecutive safe primes, however their distances (2 and 4) are singular. Cases [467, 439] and [20738027, 20738039] are pairs are both consecutive of consecutive primes and consecutive safe primes in minimal distance=12. The corresponding twins of Sophie Germain primes are [233, 239] or [1369013, 1369019] in distance 6.

%t safeQ[p_] := PrimeQ[(p-1)/2]; seq={}; c=0; p1 = p2 = 11; q1 = safeQ[p1]; While[c < 30, p2 = NextPrime[p2]; q2 = safeQ[p2]; If[q1 && q2 && p2 == p1 + 12, c++; AppendTo[seq, p1]]; p1 = p2; q1 = q2]; seq (* _Amiram Eldar_, Jan 13 2020 *)

%Y Cf. A005385, A005384, A058322, A059323, A059327.

%K nonn

%O 1,1

%A _Labos Elemer_, Jan 29 2001