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

%I A153210 #16 Sep 08 2022 08:45:39
%S A153210 7,23,47,107,167,179,263,359,383,467,479,503,587,719,839,863,887,983,
%T A153210 1187,1319,1367,1439,1487,1619,1823,1907,2027,2039,2063,2099,2207,
%U A153210 2447,2879,2903,2999,3023,3119,3167,3203,3467,3623,3779,3863,4007,4079,4127
%N A153210 Primes of the form 2*p+1 where p is prime and p+1 is not squarefree.
%C A153210 Subsequence of A005385.
%H A153210 Harvey P. Dale, <a href="/A153210/b153210.txt">Table of n, a(n) for n = 1..1000</a>
%e A153210 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.
%t A153210 lst = {}; Do[p = Prime[n]; If[PrimeQ[Floor[p/2]] && !SquareFreeQ[Ceiling[p/2]], AppendTo[lst, p]], {n, 7!}]; lst
%t A153210 2#+1&/@Select[Prime[Range[400]],!SquareFreeQ[#+1]&&PrimeQ[2#+1]&] (* _Harvey P. Dale_, Mar 17 2019 *)
%o A153210 (Magma) [ q: p in PrimesUpTo(2100) | not IsSquarefree(p+1) and IsPrime(q) where q is 2*p+1 ];
%Y A153210 Cf. A013929 (nonsquarefree numbers), A005385 (safe primes p: (p-1)/2 is also prime), A153207, A153208, A153209.
%K A153210 nonn
%O A153210 1,1
%A A153210 _Vladimir Joseph Stephan Orlovsky_, Dec 20 2008
%E A153210 Edited by _Klaus Brockhaus_, Dec 24 2008
%E A153210 First Mathematica program updated by _Jean-François Alcover_, Jul 04 2013