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Select[2#-1&/@Select[Prime[Range[1000]], !SquareFreeQ[#-1]&], PrimeQ] (* Harvey P. Dale, Aug 11 2024 *)
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Robert Israel, <a href="/A153208/b153208_1.txt">Table of n, a(n) for n = 1..10000</a>
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Robert Israel, <a href="/A153208/b153208_1.txt">Table of n, a(n) for n = 1..10000</a>
R:= NULL; count:= 0: p:= 3:
while count < 100 do
p:= nextprime(p);
if isprime(2*p-1) and not numtheory:-issqrfree(p-1) then
R:= R, 2*p-1; count:= count+1;
fi
od:
R; # Robert Israel, Nov 22 2023
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(MAGMAMagma) [ q: p in PrimesUpTo(2900) | not IsSquarefree(p-1) and IsPrime(q) where q is 2*p-1 ];
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