|
|
A153207
|
|
Primes of the form 2*p-1 where p is prime and p-1 is squarefree.
|
|
6
|
|
|
3, 5, 13, 61, 157, 277, 421, 661, 733, 877, 997, 1093, 1213, 1237, 1381, 1933, 2797, 3253, 3517, 3733, 4021, 4261, 4621, 5413, 6037, 6133, 6637, 6781, 6997, 7213, 7477, 7933, 8053, 8221, 9013, 9133, 9277, 9661, 10357, 10453, 10861, 10957, 11317, 11677
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
EXAMPLE
|
For p = 2 (the only case with p-1 odd), 2*p-1 = 3 is prime and p-1 = 1 is squarefree, so 3 is in the sequence. For p = 19, 2*p-1 = 37 is prime and p-1 = 18 is not squarefree, so 37 is not in the sequence.
|
|
MATHEMATICA
|
lst={}; Do[p = Prime[n]; If[SquareFreeQ[Floor[p/2]] && PrimeQ[Ceiling[p/2]], AppendTo[lst, p]], {n, 7!}]; lst
|
|
PROG
|
(Magma) [ q: p in PrimesUpTo(5900) | IsSquarefree(p-1) and IsPrime(q) where q is 2*p-1 ];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|