A281022 - OEIS

%I #33 Aug 14 2023 11:56:17

%S 23,47,83,167,263,359,383,467,479,503,563,587,719,839,863,887,983,

%T 1187,1283,1307,1367,1439,1523,1823,1907,2039,2063,2099,2207,2447,

%U 2459,2579,2819,2879,2903,2963,3023,3203,3623,3779,3803,3863,3947,4007,4079,4139,4283,4679,4703,4919

%N Single (or isolated or non-twin) primes that are also safe primes.

%C Primes p such that neither p - 2 nor p + 2 is prime while (p - 1) / 2 is prime.

%C It is conjectured that there are infinitely many safe primes, but this is still unproved, so it is not known whether this sequence is infinite.

%H Harvey P. Dale, <a href="/A281022/b281022.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = 2 * A230117(n+1) + 1, for n > 0.

%e 23 is a term because 23 - 2 = 21 and 23 + 2 = 25 are composite and (23 - 1) / 2 = 11 is prime.

%t Select[Prime[Range[700]],Boole[PrimeQ[{#+2,#-2,(#-1)/2}]]=={0,0,1}&] (* _Harvey P. Dale_, Aug 14 2023 *)

%o (PARI) lista(nn) = { forprime(p=11, nn, if(!isprime(p+2) && isprime((p-1)/2), print1(p, ", ")));}

%Y Cf. A005385, A007510, A230117.

%K nonn,easy

%O 1,1

%A _Altug Alkan_, Jan 13 2017