A284325 - OEIS

%I #19 Sep 30 2019 10:30:40

%S 1,1,1,1,1,2,2,5,8,8,3,3,1,1,5,9,5,12,2,7,3,12,9,9,9,14,1,14,2,18,35,

%T 56,19,38,38,26,3,13,74,12,25,12,11,8,37,79,2,43,68,3,12,46,54,7,9,9,

%U 34,4,14,49,83,3,39,87,4,10,116,128,53,13,1,32,57,92,27

%N Smallest k such that (6*k-3)*2^prime(n)-1 or (6*k-3)*2^prime(n)+1 is prime.

%C As N increases,(Sum_{n=1..N} a(n)) / (Sum_{n=1..N} prime(n)) tends to log(2)/6 as can be seen by ploting data.

%C For n from 1 to 1500 a(n)/prime(n) is always < 1.

%H Pierre CAMI, <a href="/A284325/b284325.txt">Table of n, a(n) for n = 1..1500</a>

%H Pierre CAMI, <a href="/A284325/a284325.txt">PFGW Script</a>

%t a[n_]:=Block[{k=1}, While[!PrimeQ[(6k - 3)*2^Prime[n] - 1] && !PrimeQ[(6k - 3)*2^Prime[n] + 1], k++]; k]; Table[a[n], {n, 100}] (* _Indranil Ghosh_, Mar 25 2017, translated from the PARI code *)

%t sk[n_]:=Module[{k=1,t=2^Prime[n]},While[NoneTrue[(6k-3)t+{1,-1},PrimeQ], k++]; k]; Array[sk,80] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 30 2019 *)

%o (PARI) a(n) =  my(k=1); while(!isprime((6*k-3)*2^prime(n)-1) && !isprime((6*k-3)*2^prime(n)+1), k++); k; \\ _Michel Marcus_, Mar 25 2017

%K nonn

%O 1,6

%A _Pierre CAMI_, Mar 25 2017