A153207 Primes of the form 2*p-1 where p is prime and p-1 is squarefree.

3, 5, 13, 61, 157, 277, 421, 661, 733, 877, 997, 1093, 1213, 1237, 1381, 1933, 2797, 3253, 3517, 3733, 4021, 4261, 4621, 5413, 6037, 6133, 6637, 6781, 6997, 7213, 7477, 7933, 8053, 8221, 9013, 9133, 9277, 9661, 10357, 10453, 10861, 10957, 11317, 11677

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 20 2008

Keywords

• nonn

Comments

Subsequence of A005383.

Examples

			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.
		

Crossrefs

Cf. A005117 (squarefree numbers), A005383 (numbers n such that both n and (n+1)/2 are primes), A153208, A153209, A153210.

Programs

Magma

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

Mathematica

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

Extensions

Edited by Klaus Brockhaus, Dec 24 2008

Mathematica updated by Jean-François Alcover, Jul 04 2013