A247197 - OEIS

%I #36 Sep 08 2022 08:46:09

%S 2,7,23,47,887,1297,1657,2207,2357,2753,4583,4657,6967,8353,8363,

%T 10453,12203,12343,13967,16217,16903,21737,23357,23497,25447,29017,

%U 32363,36083,40847,41603,41617,43633,45757,46933,48407,52313,60167,60457,66173,67867,71713,72497,72823,73897

%N Primes p such that 2*p^2 + 3 and 2*p^2 + 5 are also primes.

%C Primes in A247175.

%H Michael De Vlieger, <a href="/A247197/b247197.txt">Table of n, a(n) for n = 1..10000</a>

%e 2 is in this sequence because 2*2^2 + 3 = 11, 2*2^2 + 5 = 13 and 2 are all primes.

%t a247197[n_Integer] := Select[Prime /@ Range[n], And[PrimeQ[2*#^2 + 3], PrimeQ[2*#^2 + 5]] &]; a247197[7500] (* _Michael De Vlieger_, Nov 30 2014 *)

%t Select[Prime[Range[7300]],AllTrue[2#^2+{3,5},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jan 21 2019 *)

%o (Magma) [ n: n in [1..70000] | IsPrime(n) and IsPrime(2*(n^2+2)-1) and IsPrime(2*(n^2+2)+1) ];

%Y Cf. A247101, A247175, A249446.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Nov 30 2014