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

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

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

Adjacent sequences: A153205 A153206 A153207 * A153209 A153210 A153211

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 20 2008

Extensions

Edited by Klaus Brockhaus, Dec 24 2008

Mathematica updated by Jean-François Alcover, Jul 04 2013

Status

approved