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A153208
Primes of the form 2*p-1 where p is prime and p-1 is not squarefree.
7
37, 73, 193, 313, 397, 457, 541, 613, 673, 757, 1153, 1201, 1321, 1453, 1621, 1657, 1753, 1873, 1993, 2017, 2137, 2341, 2473, 2557, 2593, 2857, 2917, 3061, 3217, 3313, 4057, 4177, 4273, 4357, 4441, 4561, 4933, 5077, 5101, 5113, 5233, 5437, 5581, 5701
OFFSET
1,1
COMMENTS
Subsequence of A005383.
LINKS
EXAMPLE
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.
MAPLE
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
MATHEMATICA
lst={}; Do[p = Prime[n]; If[ !SquareFreeQ[Floor[p/2]] && PrimeQ[Ceiling[p/2]], AppendTo[lst, p]], {n, 7!}]; lst
Select[2#-1&/@Select[Prime[Range[1000]], !SquareFreeQ[#-1]&], PrimeQ] (* Harvey P. Dale, Aug 11 2024 *)
PROG
(Magma) [ q: p in PrimesUpTo(2900) | not IsSquarefree(p-1) and IsPrime(q) where q is 2*p-1 ];
CROSSREFS
Cf. A013929 (nonsquarefree numbers), A005383 (numbers n such that both n and (n+1)/2 are primes), A153207, A153209, A153210.
Sequence in context: A044023 A179579 A069204 * A128388 A137833 A083748
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by Klaus Brockhaus, Dec 24 2008
Mathematica updated by Jean-François Alcover, Jul 04 2013
STATUS
approved