OFFSET
1,1
COMMENTS
Numbers n such that n remains prime through 4 iterations of function f(x) = 2x - 1.
LINKS
EXAMPLE
Quintuplets are (1531, 3061, 6121, 12241, 24481), (6841, 13681, 27361, 54721, 109441), ...
MATHEMATICA
pQ[n_] := And @@ PrimeQ[NestList[2 # - 1 &, n, 4]]; t = {}; Do[p = Prime[n]; If[pQ[p], AppendTo[t, p]], {n, 42500}]; t (* Jayanta Basu, Jun 17 2013 *)
Select[Prime[Range[50000]], AllTrue[Rest[NestList[2#-1&, #, 4]], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 30 2019 *)
PROG
(Magma) [ p: p in PrimesUpTo(6*10^5) | forall{q: k in [1..4] | IsPrime(q) where q is 2^k*(p-1)+1} ]; // Bruno Berselli, Nov 23 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Patrick De Geest, Aug 15 2000
STATUS
approved