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 A347226 #12 Nov 20 2021 21:31:33
%S A347226 83,107,227,347,359,467,479,563,587,719,839,1187,1283,1307,1319,1439,
%T A347226 1523,1907,2027,2039,2879,2963,2999,3119,3203,3467,3803,3947,4079,
%U A347226 4283,4547,4679,4787,4799,4919,5387,5399,5483,5507,5639,5879,6599,6719,6827,7079,7187,7523
%N A347226 Safe primes (A005385) that are half-period primes (A097443).
%C A347226 Apart from 5 and 11, a safe prime p is necessarily either a full reptend prime (A001913) or a half-period prime (A097443) since (p-1) is semiprime: 2*A005384(n) (Sophie Germain primes).
%C A347226 Safe primes being full reptend primes are listed in A000353.
%C A347226 a(n) is of the form 100*k + 10*{0, 2, 4, 6, 8} + {3, 7} or 100*k + 10*{1, 3, 5, 7, 9} + 9.
%C A347226 Number of terms < 10^k: 0, 1, 11, 56, 343, 2138, 15267, 114847, 886907, 7079602, ...
%F A347226 A005385 INTERSECTION A097443.
%F A347226 a(n) == {17, 23, 29} mod 30.
%F A347226 a(n) == 11 (mod 12). - _Hugo Pfoertner_, Aug 24 2021
%e A347226 (107-1)/2 = 53 is a prime, and the periodic part of the decimal expansion of 1/107 is of length 53.
%e A347226 Hence the safe prime 107 is in the sequence.
%p A347226 select(t -> isprime(t) and isprime((t - 1)/2) and numtheory:-order(10, t) = (t - 1)/2, [seq(t, t = 3 .. 10000, 2)]);
%t A347226 Select[Prime@Range@1000,PrimeQ[(#-1)/2]&&Length[First@@RealDigits[1/#]]==(#-1)/2&] (* _Giorgos Kalogeropoulos_, Sep 14 2021 *)
%Y A347226 Cf. A005385, A097443, A005384, A000353, A001913, A002371, A006883.
%K A347226 nonn,base
%O A347226 1,1
%A A347226 _Lamine Ngom_, Aug 24 2021