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

1,1

Comments

Subsequence of A005385.

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A073577 A348230 A139830 * A185955 A158035 A101789

Adjacent sequences: A153207 A153208 A153209 * A153211 A153212 A153213

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 20 2008

Extensions

Edited by Klaus Brockhaus, Dec 24 2008

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

Status

approved