A214862 Smallest odd prime p such that 4^n - p*2^n - 1 is prime.

3, 5, 11, 5, 11, 17, 7, 5, 13, 43, 19, 11, 11, 19, 41, 7, 61, 67, 13, 31, 11, 43, 37, 101, 13, 17, 11, 67, 73, 13, 101, 13, 11, 137, 11, 31, 101, 23, 97, 11, 47, 53, 53, 17, 41, 139, 157, 7, 67, 47, 239, 127, 41, 197, 53, 13, 31, 127, 71, 191, 97, 709, 101, 41

Offset

2,1

Comments

The average of the ratio (a(n)/log(a(n)))/n for n = 2 to N tends to 0.35 as N increases.

For n <= 2000, 709 terms a(n) are <= n.

Links

Pierre CAMI, Table of n, a(n) for n = 2..2000

Example

Since 4^3 - 5*2^3 - 1 = 23 is prime, a(3) = 5.

Mathematica

sop[n_]:=Module[{c4=4^n-1, c2=2^n, i=3}, While[!PrimeQ[c4-i*c2], i= NextPrime[ i]]; i]; Array[sop, 70, 2] (* Harvey P. Dale, Oct 28 2013 *)

Prog

(PFGW Scriptify)
SCRIPT
DIM n, 1
DIM k
DIMS t
LABEL a
SET n, n+1
IF n>2000 THEN END
SET k, 1
LABEL b
SET k, k+1
SETS t, %d, %d\,; k; n
PRP 4^n-p(k)*2^n-1, t
IF ISPRP THEN GOTO a
GOTO b
(PARI)
N=10^6;  default(primelimit, N);
a(n) = {
  my(n4=4^n, n2=2^n);
  forprime (p=3, N,
    if ( isprime(n4-p*n2-1), return(p) )
  );
  return(-1);
} /* Joerg Arndt, Mar 11 2013 */

Crossrefs

Sequence in context: A258862 A139430 A143386 * A151885 A137656 A046228

Adjacent sequences: A214859 A214860 A214861 * A214863 A214864 A214865

Keyword

nonn

Author

Pierre CAMI, Mar 09 2013

Status

approved