cp's OEIS Frontend

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

%I A225911 #30 Jun 17 2025 16:15:58
%S A225911 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,
%T A225911 3,28,48,8,11,31,17,102,17,7,17,8,2,35,13,135,33,72,12,2,18,3,26,17,
%U A225911 38,16,51,12,2,2,2,40,103,45,26,40,16,3,10,26,10,8,2,11
%N A225911 Smallest k such that k*6^n+1 is prime.
%C A225911 In average k~0.6*n and 0 < k < 8*n until a proof that k may be > 8*n.
%C A225911 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
%H A225911 Pierre CAMI, <a href="/A225911/b225911.txt">Table of n, a(n) for n = 1..3000</a>
%H A225911 <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>
%e A225911 6^1+1=7 is prime, so  a(1)=1;
%e A225911 6^2+1=37 is prime, so a(2)=1;
%e A225911 6^3+1=217 is composite, 2*6^3+1=433 is prime, so a(3)=2.
%t A225911 skp[n_]:=Module[{k=1,c=6^n},While[!PrimeQ[k*c+1],k++];k]; Array[skp,80] (* _Harvey P. Dale_, Jun 17 2025 *)
%o A225911 (PFGW & SCRIPTIFY)
%o A225911 SCRIPT
%o A225911 DIM n,0
%o A225911 DIM k
%o A225911 DIMS t
%o A225911 OPENFILEOUT myf,a(n).txt
%o A225911 LABEL a
%o A225911 SET n,n+1
%o A225911 IF n>3000 THEN END
%o A225911 SET k,0
%o A225911 LABEL b
%o A225911 SET k,k+1
%o A225911 SETS t,%d,%d\,;n;k
%o A225911 PRP k*6^n+1,t
%o A225911 IF ISPRP THEN GOTO c
%o A225911 GOTO b
%o A225911 LABEL c
%o A225911 WRITE myf,t
%o A225911 GOTO a
%o A225911 (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
%o A225911 (PARI) a(n)=my(k);while(!ispseudoprime(k++*6^n+1),);k \\ _Charles R Greathouse IV_, May 20 2013
%Y A225911 Cf. A225941, A035050.
%K A225911 nonn
%O A225911 1,3
%A A225911 _Pierre CAMI_, May 20 2013