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A239676 Least k such that k*3^n+1 is prime.

%I A239676 #26 May 22 2025 10:21:37
%S A239676 1,2,2,4,2,2,2,8,6,2,8,28,10,12,4,4,2,2,10,20,26,24,8,48,16,34,14,14,
%T A239676 18,6,2,26,26,14,22,26,16,22,12,4,62,64,68,88,70,56,34,96,32,50,20,24,
%U A239676 8,6,2,18,6,2,8,6,2,42,14,18,6,2,98,66,22,70,74,80,68,52
%N A239676 Least k such that k*3^n+1 is prime.
%C A239676 All numbers in this sequence, except for a(0), are even.
%H A239676 Marius A. Burtea, <a href="/A239676/b239676.txt">Table of n, a(n) for n = 0..1000</a>
%e A239676 1*3^1+1 = 4 is not prime. 2*3^1+1 = 7 is prime. Thus, a(1) = 2.
%e A239676 1*3^3+1 = 28 is not prime. 2*3^3+1 = 57 is not prime. 3*3^3+1 = 82 is not prime. 4*3^3+1 = 109 is prime. Thus, a(3) = 4.
%t A239676 lk[n_]:=Module[{k=1,t=3^n},While[!PrimeQ[k*t+1],k++];k]; Array[lk,80,0] (* _Harvey P. Dale_, May 11 2025 *)
%o A239676 (Python)
%o A239676 import sympy
%o A239676 from sympy import isprime
%o A239676 def Pow3(n):
%o A239676   for k in range(10**4):
%o A239676     if isprime(k*(3**n)+1):
%o A239676       return n
%o A239676 n = 1
%o A239676 while n < 100:
%o A239676   print(Pow3(n))
%o A239676   n += 1
%o A239676 (PARI)
%o A239676 for(n=0, 100, k=0; while(!isprime(k*3^n+1), k++); print1(k, ", ")) \\ _Colin Barker_, Mar 24 2014
%o A239676 (Magma) sol:=[];m:=1; for n in [0..73] do k:=0; while not IsPrime(k*3^n+1) do k:=k+1; end while; sol[m]:=k; m:=m+1; end for; sol; // _Marius A. Burtea_, Jun 05 2019
%Y A239676 Cf. A003306 (where k=2), A035050 (k*2^n+1 is prime).
%K A239676 nonn
%O A239676 0,2
%A A239676 _Derek Orr_, Mar 23 2014