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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Subsequence of A005385.
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by Klaus Brockhaus, Dec 24 2008
First Mathematica program updated by Jean-François Alcover, Jul 04 2013
STATUS
approved

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Last modified April 21 23:01 EDT 2024. Contains 371886 sequences. (Running on oeis4.)