A057328 First member of a prime 5-tuple in a 2p-1 progression.

1531, 6841, 15391, 16651, 33301, 44371, 57991, 66601, 83431, 105871, 145021, 150151, 165901, 199621, 209431, 212851, 231241, 242551, 291271, 319681, 331801, 346141, 377491, 381631, 385591, 445741, 451411, 478801, 481021, 506791, 507781

Offset: 1

Author

Patrick De Geest, Aug 15 2000

Keywords

• nonn

Comments

Numbers n such that n remains prime through 4 iterations of function f(x) = 2x - 1.

Examples

			Quintuplets are (1531, 3061, 6121, 12241, 24481), (6841, 13681, 27361, 54721, 109441), ...
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to primes in arithmetic progressions

Crossrefs

Cf. A005382, A005383, A057326, A057327, A057329, A057330, A005603.

Programs

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

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 *)