A059395 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.

467, 1307, 2447, 5087, 5927, 12527, 18947, 44687, 78467, 83207, 118787, 143687, 164987, 196907, 204587, 207227, 208787, 229487, 236507, 257627, 275987, 297707, 330887, 339827, 367007, 369647, 394007, 454907, 458807, 474347, 534827, 536087

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

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.

Mathematica

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 *)

Crossrefs

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

Sequence in context: A034593 A036339 A036340 * A266163 A221238 A114135

Adjacent sequences: A059392 A059393 A059394 * A059396 A059397 A059398

Keyword

nonn

Author

Labos Elemer, Jan 29 2001

Status

approved