A153210 Primes of the form 2*p+1 where p is prime and p+1 is not squarefree.

7, 23, 47, 107, 167, 179, 263, 359, 383, 467, 479, 503, 587, 719, 839, 863, 887, 983, 1187, 1319, 1367, 1439, 1487, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2879, 2903, 2999, 3023, 3119, 3167, 3203, 3467, 3623, 3779, 3863, 4007, 4079, 4127

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 20 2008

Keywords

• nonn

Comments

Subsequence of A005385.

Examples

			For p = 2 (the only case with p+1 odd), 2*p+1 = 5 is prime but p+1 = 3 is squarefree, so 5 is not in the sequence. For p = 3, 2*p+1 = 7 is prime and p+1 = 4 is not squarefree, so 7 is in the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A013929 (nonsquarefree numbers), A005385 (safe primes p: (p-1)/2 is also prime), A153207, A153208, A153209.

Programs

Magma

[ q: p in PrimesUpTo(2100) | not IsSquarefree(p+1) and IsPrime(q) where q is 2*p+1 ];

Mathematica

lst = {}; Do[p = Prime[n]; If[PrimeQ[Floor[p/2]] && !SquareFreeQ[Ceiling[p/2]], AppendTo[lst, p]], {n, 7!}]; lst
2#+1&/@Select[Prime[Range[400]],!SquareFreeQ[#+1]&&PrimeQ[2#+1]&] (* Harvey P. Dale, Mar 17 2019 *)

Extensions

Edited by Klaus Brockhaus, Dec 24 2008

First Mathematica program updated by Jean-François Alcover, Jul 04 2013