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A153208 Primes of the form 2*p-1 where p is prime and p-1 is not squarefree.

%I A153208 #16 Aug 11 2024 10:58:13
%S A153208 37,73,193,313,397,457,541,613,673,757,1153,1201,1321,1453,1621,1657,
%T A153208 1753,1873,1993,2017,2137,2341,2473,2557,2593,2857,2917,3061,3217,
%U A153208 3313,4057,4177,4273,4357,4441,4561,4933,5077,5101,5113,5233,5437,5581,5701
%N A153208 Primes of the form 2*p-1 where p is prime and p-1 is not squarefree.
%C A153208 Subsequence of A005383.
%H A153208 Robert Israel, <a href="/A153208/b153208.txt">Table of n, a(n) for n = 1..10000</a>
%e A153208 For p = 2 (the only case with p-1 odd), 2*p-1 = 3 is prime but p-1 = 1 is squarefree, so 3 is not in the sequence. For p = 19, 2*p-1 = 37 is prime and p-1 = 18 is not squarefree, so 37 is in the sequence.
%p A153208 R:= NULL; count:= 0: p:= 3:
%p A153208 while count < 100 do
%p A153208   p:= nextprime(p);
%p A153208   if isprime(2*p-1) and not numtheory:-issqrfree(p-1) then
%p A153208      R:= R, 2*p-1; count:= count+1;
%p A153208   fi
%p A153208 od:
%p A153208 R; # _Robert Israel_, Nov 22 2023
%t A153208 lst={}; Do[p = Prime[n]; If[ !SquareFreeQ[Floor[p/2]] && PrimeQ[Ceiling[p/2]], AppendTo[lst, p]], {n, 7!}]; lst
%t A153208 Select[2#-1&/@Select[Prime[Range[1000]],!SquareFreeQ[#-1]&],PrimeQ] (* _Harvey P. Dale_, Aug 11 2024 *)
%o A153208 (Magma) [ q: p in PrimesUpTo(2900) | not IsSquarefree(p-1) and IsPrime(q) where q is 2*p-1 ];
%Y A153208 Cf. A013929 (nonsquarefree numbers), A005383 (numbers n such that both n and (n+1)/2 are primes), A153207, A153209, A153210.
%K A153208 nonn
%O A153208 1,1
%A A153208 _Vladimir Joseph Stephan Orlovsky_, Dec 20 2008
%E A153208 Edited by _Klaus Brockhaus_, Dec 24 2008
%E A153208 Mathematica updated by _Jean-François Alcover_, Jul 04 2013