A240166 Smallest prime number P such that 2*P^(2*n)-1 is a prime number.

2, 2, 2, 3, 13, 2, 7, 2, 2, 3, 79, 5, 83, 1427, 2, 83, 47, 7, 31, 139, 23, 53, 7, 373, 193, 71, 5, 3, 463, 2, 3, 13, 281, 3, 281, 59, 17, 13, 1399, 7, 61, 163, 151, 2, 103, 479, 89, 5, 127, 421, 457, 857, 2, 43, 101, 349, 359, 2243, 13, 13, 17, 1451, 2

Offset

1,1

Comments

a(n) = 2 when 2*n + 1 is a prime Mersenne exponent (A000043).

Links

Pierre CAMI, Table of n, a(n) for n = 1..700

Example

2*2^(2*1) - 1 = 7 prime so a(1) = 2.
2*2^(2*2) - 1 = 31 prime so a(2) = 2.
2*2^(2*3) - 1 = 127 prime so a(3) = 2.

Maple

A:= proc(n)
local p;
p:= 2;
while not isprime(2*p^(2*n)-1) do p:= nextprime(p) od:
p;
end proc:
seq(A(n), n=1..100); # Robert Israel, Sep 14 2014

Mathematica

a240166[n_Integer] := Module[{p = 1},
  While[! PrimeQ[2*Prime[p]^(2*n) - 1], p++]; Prime[p]]; a240166 /@ Range[120] (* Michael De Vlieger, Aug 12 2014 *)

Prog

(PFGW & SCRIPT)
SCRIPT
DIM i
DIM n, 0
DIM k
DIMS t
OPENFILEOUT myf, a(n).txt
LABEL loop1
SET n, n+1
SET i, 0
LABEL loop2
SET i, i+1
SETS t, %d, %d\ ; n; p(i)
PRP 2*p(i)^(2*n)-1, t
IF ISPRP THEN GOTO a
GOTO loop2
LABEL a
WRITE myf, t
GOTO loop1
(PARI) a(n) = p=2; while(!ispseudoprime(2*p^(2*n)-1), p=nextprime(p+1)); p
vector(70, n, a(n)) \\ Colin Barker, Aug 02 2014

Crossrefs

Cf. A000043.

Sequence in context: A238188 A360693 A051007 * A346801 A326375 A358318

Adjacent sequences: A240163 A240164 A240165 * A240167 A240168 A240169

Keyword

nonn

Author

Pierre CAMI, Aug 02 2014

Status

approved