A153207 - OEIS

%I #9 Sep 08 2022 08:45:39

%S 3,5,13,61,157,277,421,661,733,877,997,1093,1213,1237,1381,1933,2797,

%T 3253,3517,3733,4021,4261,4621,5413,6037,6133,6637,6781,6997,7213,

%U 7477,7933,8053,8221,9013,9133,9277,9661,10357,10453,10861,10957,11317,11677

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

%C Subsequence of A005383.

%e For p = 2 (the only case with p-1 odd), 2*p-1 = 3 is prime and p-1 = 1 is squarefree, so 3 is in the sequence. For p = 19, 2*p-1 = 37 is prime and p-1 = 18 is not squarefree, so 37 is not in the sequence.

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

%o (Magma) [ q: p in PrimesUpTo(5900) | IsSquarefree(p-1) and IsPrime(q) where q is 2*p-1 ];

%Y Cf. A005117 (squarefree numbers), A005383 (numbers n such that both n and (n+1)/2 are primes), A153208, A153209, 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