login
Numbers k such that 24*k + 5 and 24*k + 7 are twin primes.
9

%I #19 Sep 08 2022 08:45:33

%S 0,1,4,6,8,11,19,34,44,51,53,54,78,81,83,89,93,96,99,106,116,141,144,

%T 148,149,159,163,173,176,184,188,193,209,228,229,239,258,261,279,286,

%U 306,316,323,328,331,351,358,368,369,389,393,394,401,403,418,429,446

%N Numbers k such that 24*k + 5 and 24*k + 7 are twin primes.

%C 1/3 of number k such that 8k + 5 and 8k + 7 are primes.

%C All numbers in A125821 are divisible by 3.

%H Amiram Eldar, <a href="/A139404/b139404.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A125821(n)/3.

%e 0 is in the sequence since 24*0 + 5 = 5 and 24*0 + 7 = 7 are twin primes.

%t a = {}; Do[If[PrimeQ[8 n + 5] && PrimeQ[8 n + 3] && PrimeQ[n],AppendTo[a, n]], {n, 1, 10000}]; a

%t Select[Range[0,500],AllTrue[24#+{5,7},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Mar 08 2019 *)

%o (Magma) [n: n in [0..5000] |IsPrime(24*n+5)and IsPrime(24*n+7)] // _Vincenzo Librandi_, Nov 24 2010

%Y Cf. A125822, A139402, A139404.

%K nonn

%O 1,3

%A _Artur Jasinski_, Apr 19 2008

%E a(1) = 0 inserted by _Vincenzo Librandi_, Mar 25 2010