A153209 - OEIS

%I #14 Aug 02 2024 13:23:15

%S 5,11,59,83,227,347,563,1019,1283,1307,1523,2459,2579,2819,2963,3803,

%T 3947,4259,4547,5387,5483,6779,6827,7187,8147,9587,10667,10883,11003,

%U 12107,12227,12539,12659,13043,13163,14243,14387,15683,16139,16187

%N Primes of the form 2*p+1 where p is prime and p+1 is squarefree.

%C Subsequence of A005385.

%H Harvey P. Dale, <a href="/A153209/b153209.txt">Table of n, a(n) for n = 1..1000</a>

%e For p = 2 (the only case with p+1 odd), 2*p+1 = 5 is prime and p+1 = 3 is squarefree, so 5 is in the sequence. For p = 3, 2*p+1 = 7 is prime and p+1 = 4 is not squarefree, so 7 is not in the sequence.

%t lst = {}; Do[p = Prime[n]; If[PrimeQ[Floor[p/2]] && SquareFreeQ[Ceiling[p/2]], AppendTo[lst, p]], {n, 7!}]; lst

%t Select[2#+1&/@Select[Prime[Range[2000]],SquareFreeQ[#+1]&],PrimeQ] (* _Harvey P. Dale_, Aug 02 2024 *)

%o (Magma) [ q: p in PrimesUpTo(8100) | IsSquarefree(p+1) and IsPrime(q) where q is 2*p+1 ];

%Y Cf. A005117 (squarefree numbers), A005385 (safe primes p: (p-1)/2 is also prime), A153207, A153208, A153210.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Dec 20 2008

%E Edited by _Klaus Brockhaus_, Dec 24 2008

%E Mathematica updated by _Jean-François Alcover_, Jul 04 2013