|
Search: id:A153210
|
|
|
| A153210 |
|
Primes of the form 2*p+1 where p is prime and p+1 is not square-free. |
|
+0
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; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Subsequence of A005385.
|
|
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
|
<< NumberTheory`NumberTheoryFunctions` lst={}; Do[p=Prime[n]; If[PrimeQ[Floor[p/2]]&&!SquareFreeQ[Ceiling[p/2]], AppendTo[lst, p]], {n, 7!}]; lst
|
|
PROGRAM
|
(MAGMA) [ q: p in PrimesUpTo(2100) | not IsSquarefree(p+1) and IsPrime(q) where q is 2*p+1 ];
|
|
CROSSREFS
|
Cf. A013929 (not square-free numbers), A005385 (safe primes p: (p-1)/2 is also prime), A153207, A153208, A153209.
Sequence in context: A002146 A073577 A139830 this_sequence A158035 A101789 A162290
Adjacent sequences: A153207 A153208 A153209 this_sequence A153211 A153212 A153213
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 20 2008
|
|
EXTENSIONS
|
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 24 2008
|
|
|
Search completed in 0.002 seconds
|
