OFFSET
1,1
COMMENTS
Subsequence of A005383.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
For p = 2 (the only case with p-1 odd), 2*p-1 = 3 is prime but p-1 = 1 is squarefree, so 3 is not in the sequence. For p = 19, 2*p-1 = 37 is prime and p-1 = 18 is not squarefree, so 37 is in the sequence.
MAPLE
R:= NULL; count:= 0: p:= 3:
while count < 100 do
p:= nextprime(p);
if isprime(2*p-1) and not numtheory:-issqrfree(p-1) then
R:= R, 2*p-1; count:= count+1;
fi
od:
R; # Robert Israel, Nov 22 2023
MATHEMATICA
lst={}; Do[p = Prime[n]; If[ !SquareFreeQ[Floor[p/2]] && PrimeQ[Ceiling[p/2]], AppendTo[lst, p]], {n, 7!}]; lst
Select[2#-1&/@Select[Prime[Range[1000]], !SquareFreeQ[#-1]&], PrimeQ] (* Harvey P. Dale, Aug 11 2024 *)
PROG
(Magma) [ q: p in PrimesUpTo(2900) | not IsSquarefree(p-1) and IsPrime(q) where q is 2*p-1 ];
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Dec 20 2008
EXTENSIONS
Edited by Klaus Brockhaus, Dec 24 2008
Mathematica updated by Jean-François Alcover, Jul 04 2013
STATUS
approved