OFFSET
1,1
COMMENTS
Subsequence of A056798.
From R. J. Mathar, Jul 11 2011: (Start)
For odd k >= 3, (1+p^k)/2 is not prime. [Sketch of proof: for p=2 it is not integer. Otherwise for odd k, (1+p^k)/(1+p) = Sum_{j=0..k-1} (-p)^j, an integer, so 1+p^k is a multiple of 1+p. For odd p, (1+p^k)/2 is a multiple of (1+p)/2 and therefore composite.] (End)
LINKS
Klaus Brockhaus, Table of n, a(n) for n = 1..1000
MATHEMATICA
Select[Union[Flatten[Table[Prime[n]^k, {n, 142}, {k, 0, 32, 2}]]], PrimeQ[(# + 1)/2] &] (* Alonso del Arte, Jul 05 2011 *)
PROG
(Magma) e:=20; u:=1000; z:=Min(2^e, u^2); S:=[ q: p in PrimesUpTo(u), k in [2..e by 2] | q le z and IsEven(1+q) and IsPrime((1+q) div 2) where q is p^k ]; Sort(~S); S;
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Jul 05 2011
STATUS
approved