A225911 Smallest k such that k*6^n+1 is prime.

1, 1, 2, 1, 10, 3, 3, 3, 12, 2, 2, 15, 17, 11, 3, 8, 2, 10, 12, 2, 73, 35, 21, 11, 18, 3, 12, 2, 3, 28, 48, 8, 11, 31, 17, 102, 17, 7, 17, 8, 2, 35, 13, 135, 33, 72, 12, 2, 18, 3, 26, 17, 38, 16, 51, 12, 2, 2, 2, 40, 103, 45, 26, 40, 16, 3, 10, 26, 10, 8, 2, 11

Offset

1,3

Comments

In average k~0.6*n and 0 < k < 8*n until a proof that k may be > 8*n.

Dirichlet's theorem proves that a(n) exists for each n. Linnik's theorem gives bounds; in particular the version due to Xylouris gives a(n) << 1855^n. - Charles R Greathouse IV, May 20 2013

Links

Pierre CAMI, Table of n, a(n) for n = 1..3000

Index entries for sequences related to primes in arithmetic progressions

Example

6^1+1=7 is prime, so  a(1)=1;
6^2+1=37 is prime, so a(2)=1;
6^3+1=217 is composite, 2*6^3+1=433 is prime, so a(3)=2.

Prog

(PFGW & SCRIPTIFY)
SCRIPT
DIM n, 0
DIM k
DIMS t
OPENFILEOUT myf, a(n).txt
LABEL a
SET n, n+1
IF n>3000 THEN END
SET k, 0
LABEL b
SET k, k+1
SETS t, %d, %d\,; n; k
PRP k*6^n+1, t
IF ISPRP THEN GOTO c
GOTO b
LABEL c
WRITE myf, t
GOTO a
(Magma) S:=[]; for n in [1..100] do k:=1; while not IsPrime(k*6^n+1) do k:=k+1; end while; Append(~S, k); end for; S; // Bruno Berselli, May 20 2013
(PARI) a(n)=my(k); while(!ispseudoprime(k++*6^n+1), ); k \\ Charles R Greathouse IV, May 20 2013

Crossrefs

Cf. A225941, A035050.

Sequence in context: A247236 A011268 A332080 * A163235 A142963 A099755

Adjacent sequences: A225908 A225909 A225910 * A225912 A225913 A225914

Keyword

nonn

Author

Pierre CAMI, May 20 2013

Status

approved