A284325 Smallest k such that (6*k-3)*2^prime(n)-1 or (6*k-3)*2^prime(n)+1 is prime.

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

Offset: 1

Author

Pierre CAMI, Mar 25 2017

Keywords

• nonn

Comments

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.

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

Links

• Pierre CAMI, Table of n, a(n) for n = 1..1500
• Pierre CAMI, PFGW Script

Programs

Mathematica

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 *)
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 *)

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