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Smallest k not divisible by 3 such that k*3^n + 1 is prime.
3

%I #24 Dec 27 2017 03:14:59

%S 2,2,4,2,2,2,8,8,2,8,28,10,64,4,4,2,2,10,20,26,56,8,104,16,34,14,14,

%T 20,26,2,26,26,14,22,26,16,22,50,4,62,64,68,88,70,56,34,146,32,50,20,

%U 314,8,40,2,70,22,2,8,40,2,64,14,136,100,2

%N Smallest k not divisible by 3 such that k*3^n + 1 is prime.

%C The ratio (Sum_(n=1..t) a(n)) / (Sum_(n=1..t) n) tends to log(3) as t increases.

%C Differs from A239676 when A239676(n) is a multiple of 3. - _Michel Marcus_, Nov 25 2017

%H Pierre CAMI, <a href="/A295639/b295639.txt">Table of n, a(n) for n = 1..4000</a>

%p f:= proc(n) local i,j,k,t;

%p t:= 3^n;

%p for i from 0 do

%p for j in [2,4] do

%p if isprime((6*i+j)*t+1) then return 6*i+j fi

%p od od

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Dec 14 2017

%t f[n_] := Block[{k = 2}, While[If[Mod[k, 3] == 0, k+=2]; ! PrimeQ[k*3^n + 1], k+=2]; k]; Array[f, 65] (* _Robert G. Wilson v_, Dec 12 2017 *)

%o (PARI) a(n) = {k = 1; while (!isprime(k*3^n+1), k++; if (! (k%3), k++)); k;} \\ _Michel Marcus_, Nov 25 2017

%Y Cf. A057778, A239676, A295640, A295641.

%K nonn

%O 1,1

%A _Pierre CAMI_, Nov 25 2017