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A059327 a(n) is smallest safe prime (A005385) such that a(n) + 12*n is the next safe prime, i.e., x = (a(n) - 1)/2 and x + 6*n are closest Sophie Germain primes.

%I A059327 #14 Jan 01 2024 14:10:47
%S A059327 11,23,227,179,107,1367,263,887,2099,719,587,8819,3467,1019,10163,
%T A059327 27827,1619,7823,27299,2207,44267,3203,7247,5099,11807,45887,18119,
%U A059327 15803,79559,13163,40127,42839,20663,79979,17483,53267,47963,33863
%N A059327 a(n) is smallest safe prime (A005385) such that a(n) + 12*n is the next safe prime, i.e., x = (a(n) - 1)/2 and x + 6*n are closest Sophie Germain primes.
%H A059327 Amiram Eldar, <a href="/A059327/b059327.txt">Table of n, a(n) for n = 1..1000</a>
%e A059327 {11, 23, 227, 179, 107, ...} are the smallest safe primes such that {11+12, 23+24, 227+36, 179+48, 107+60, ...} = {23, 47, 263, 227, 167, ...} are their next safe primes to which the corresponding Sophie Germain primes are {11, 23, 131, 113, 83, ...} respectively.
%t A059327 safeQ[p_] := PrimeQ[(p-1)/2]; max = 38; seq = Table[0, {max}]; c=0; p1 = p2 = 11; While[c < max, p2 = NextPrime[p2]; If[safeQ[p2], d = (p2 - p1)/12; If[d <= max && seq[[d]] == 0, c++; seq[[d]] = p1]; p1 = p2]]; seq (* _Amiram Eldar_, Jan 13 2020 *)
%Y A059327 Cf. A005384, A005385, A033299.
%K A059327 nonn
%O A059327 1,1
%A A059327 _Labos Elemer_, Jan 26 2001
%E A059327 Offset corrected by _Amiram Eldar_, Jan 13 2020