A145471 - OEIS

%I #21 Sep 08 2022 08:45:38

%S 5,17,29,41,53,89,101,113,137,173,197,257,269,293,353,389,449,461,509,

%T 521,557,617,701,761,773,797,857,881,929,953,977,1013,1109,1181,1193,

%U 1229,1277,1289,1301,1361,1433,1481,1613,1637,1709,1721,1877,1889,1901

%N Primes p such that (5+p)/2 is prime.

%C All these primes are congruent to 1 mod 4 and to 5 mod 12.

%H Robert Israel, <a href="/A145471/b145471.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 2*A063909(n)-5. - _Robert Israel_, Feb 24 2016

%p select(t -> isprime(t) and isprime((t+5)/2), [seq(i, i=5..1000, 12)]); # _Robert Israel_, Feb 24 2016

%t aa = {}; k = 5; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa

%t Select[Prime[Range[500]],PrimeQ[(5+#)/2]&]  (* _Harvey P. Dale_, Apr 23 2011 *)

%o (PARI) forprime(p=2,1e4,if(p%12!=5,next);if(isprime(p\2+3),print1(p", "))) \\ _Charles R Greathouse IV_, Jul 16 2011

%o (Magma) [p: p in PrimesInInterval(3,2000) | IsPrime((5+p) div 2)]; // _Vincenzo Librandi_, Feb 25 2016

%Y Cf. A063909, A092109.

%Y Subsequence of A040117. - _Zak Seidov_, Feb 21 2016

%K nonn

%O 1,1

%A _Artur Jasinski_, Oct 11 2008