A245600 Smallest prime Q such that prime(n)*(2*Q)^prime(n)-1 is prime.

2, 2, 2, 7, 5, 109, 23, 3, 2, 2843, 1879, 643, 809, 1153, 653, 2969, 4679, 241, 19, 9749, 6247, 13, 2003, 5639, 3061, 13799, 73, 2, 6733, 113, 2917, 24977, 2411, 19, 6473, 12457, 3187, 6133, 4967, 22643, 26723, 1279, 2837, 5347, 353, 9721, 19, 433

Offset

1,1

Links

Pierre CAMI and Jens Kruse Andersen, Table of n, a(n) for n = 1..200 (first 100 terms from Pierre CAMI)

Example

2*(2*2)^2-1 = 31 prime so a(1) = 2.
3*(2*2)^3-1 = 191 prime so a(2) = 2.

Maple

A:= proc(n)
local p, q;
p:= ithprime(n);
q:= 1;
do
  q:= nextprime(q);
  if isprime(p*(2*q)^p-1) then return(q) fi
od:
end proc:
seq(A(n), n=1..50); # Robert Israel, Aug 05 2014

Mathematica

a245600[n_Integer] := Catch[
  Do[
   If[And[PrimeQ[Q], PrimeQ[Prime[n]*(2*Q)^Prime[n] - 1]] == True,
    Throw[Q]],
   {Q, 1000000}]
  ]; Map[a245600, Range[50]] (* Michael De Vlieger, Aug 03 2014 *)

Prog

(PFGW & SCRIPT)
SCRIPT
DIM i, 0
DIM n
DIMS t
OPENFILEOUT myf, b(n).txt
LABEL loop1
SET i, i+1
IF i>100 THEN END
SET n, 0
LABEL loop2
SET n, n+1
SETS t, %d, %d\,; p(i); p(n)
PRP p(i)*(2*p(n))^p(i)-1, t
IF ISPRP THEN GOTO a
GOTO loop2
LABEL a
WRITE myf, t
GOTO loop1
(PARI) a(n)=for(k=1, 10^5, if(ispseudoprime(prime(n)*(2*prime(k))^prime(n)-1), return(prime(k))))
n=1; while(n<100, print1(a(n), ", "); n++) \\ Derek Orr, Jul 27 2014

Crossrefs

Cf. A245597, A245598, A245601.

Sequence in context: A279967 A094246 A169592 * A266689 A265988 A340976

Adjacent sequences: A245597 A245598 A245599 * A245601 A245602 A245603

Keyword

nonn

Author

Pierre CAMI, Jul 27 2014

Status

approved