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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 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

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