

A153210


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


7



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
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OFFSET

1,1


COMMENTS



LINKS



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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



