OFFSET
1,5
COMMENTS
As N increases, (Sum_{n=1..N} a(n)) / (Sum_{n=1..N} n) tends to log(2)/3 as seen by plotting data; this is consistent with the prime number theorem as the probability that (6*x-3)*2^n - 1 is prime is ~ 3/(n*log(2)) if n is great enough, so after n*log(2)/3 try n*log(2)/3*(3/n*log(2))=1.
For n=1 to 14000, a(n)/n is always < 3.
LINKS
Pierre CAMI, Table of n, a(n) for n = 1..14000
MATHEMATICA
Table[k = 1; While[! PrimeQ[(6 k - 3)*2^n - 1], k++]; k, {n, 76}] (* Michael De Vlieger, Apr 27 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Pierre CAMI, Apr 27 2017
STATUS
approved