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A239676 Least k such that k*3^n+1 is prime. 2

%I #22 Sep 08 2022 08:46:07

%S 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 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 8,6,2,18,6,2,8,6,2,42,14,18,6,2,98,66,22,70,74,80,68,52

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

%C All numbers in this sequence, except for a(0), are even.

%H Marius A. Burtea, <a href="/A239676/b239676.txt">Table of n, a(n) for n = 0..1000</a>

%e 1*3^1+1 = 4 is not prime. 2*3^1+1 = 7 is prime. Thus, a(1) = 2.

%e 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.

%o (Python)

%o import sympy

%o from sympy import isprime

%o def Pow3(n):

%o ..for k in range(10**4):

%o ....if isprime(k*(3**n)+1):

%o ......return n

%o n = 1

%o while n < 100:

%o ..print(Pow3(n))

%o ..n += 1

%o (PARI)

%o for(n=0, 100, k=0; while(!isprime(k*3^n+1), k++); print1(k, ", ")) \\ _Colin Barker_, Mar 24 2014

%o (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 Cf. A003306 (where k=2), A035050 (k*2^n+1 is prime).

%K nonn

%O 0,2

%A _Derek Orr_, Mar 23 2014

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