OFFSET
1,2
COMMENTS
According to the conjecture in A236389, this sequence should have infinitely many terms.
The prime 2^(a(31))*p(a(31)) + 1 = 2^(37190)*p(37190) + 1 has 11405 decimal digits.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..31
EXAMPLE
a(1) = 1 since 2^1*p(1) + 1 = 2*1 + 1 = 3 is prime.
MATHEMATICA
q[n_]:=PrimeQ[2^n*PartitionsP[n]+1]
n=0; Do[If[q[m], n=n+1; Print[n, " ", m]], {m, 1, 10000}]
Select[Range[40000], PrimeQ[2^# PartitionsP[#]+1]&] (* Harvey P. Dale, Dec 30 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jan 24 2014
STATUS
approved