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A247010 Primes p such that (p-3)/2 and 2*p+3 are both prime.

%I A247010 #21 Sep 08 2022 08:46:09
%S A247010 7,13,17,29,89,97,137,197,229,277,337,349,397,557,617,797,929,937,
%T A247010 1117,1217,1237,1777,2129,2309,2437,2477,2617,2749,2857,2909,3049,
%U A247010 3109,3137,3329,3389,4057,4229,4289,4409,5237,5297,5417,5557,5717,5857,6689
%N A247010 Primes p such that (p-3)/2 and 2*p+3 are both prime.
%C A247010 A023204 INTERSECT A089531. After 7, all terms are obviously in A002144.
%C A247010 Conjecture: the sequence is infinite.
%H A247010 Vincenzo Librandi, <a href="/A247010/b247010.txt">Table of n, a(n) for n = 1..1000</a>
%F A247010 a(n) = 2*A023242(n) + 3. [_Bruno Berselli_, Sep 09 2014]
%t A247010 Select[Prime[Range[900]], And@@PrimeQ/@{(# - 3)/2, 2 # + 3} &]
%o A247010 (Magma) [p: p in PrimesUpTo(7000) | IsPrime((p-3)div 2) and IsPrime(2*p+3)];
%o A247010 (Sage)
%o A247010 def t(i): return 2*i+3
%o A247010 [t(p) for p in primes(5000) if is_prime(t(p)) and is_prime(t(t(p)))] # _Bruno Berselli_, Sep 09 2014
%o A247010 (PARI) is(n)=isprime(n) && isprime(2*n+3) && isprime((n-3)\2) \\ _Charles R Greathouse IV_, Sep 09 2014
%Y A247010 Cf. A023204, A023242, A089531.
%K A247010 nonn,easy,less
%O A247010 1,1
%A A247010 _Vincenzo Librandi_, Sep 09 2014