OFFSET
1,1
COMMENTS
These numbers are all of the form 4n+1.
k needs to be a power of two. The sequence of the associated k is 2, 2, 4, 4, 2, 4, 4, 8, 4, 4, 64, 4, 2, 0, 32, 4, 4, 4, 0, 0, 0, 8, 0, 0, 8, 4, 8, 4, 2, 4, 0, 32, 0, 2, 8, 2, ... where 0 is inserted if a(n) does not appear to exist. - Robert G. Wilson v, Aug 02 2018
It seems likely that a(14) does not exist. No k <= 2^15 works. - Don Reble and Robert Israel, Aug 02 2018
LINKS
Zak Seidov, query about (3^n + 5^n)/2 is prime in seqfan 9/10/06.
MAPLE
A121710 := proc(n)
local p1, p2, k, a ;
p1 := ithprime(n+1) ;
p2 := nextprime(p1) ;
for k from 1 do
a := (p1^k+p2^k)/2 ;
if type(a, 'integer') and isprime(a) then
return a;
end if;
end do:
end proc:
for n from 1 do
printf("%d %d\n", n, A121710(n)) ;
end do: # R. J. Mathar, Aug 02 2018
PROG
(PARI) g(n, a, b) = for(x=1, n, y=(a^x+b^x)/2; if(ispseudoprime(y), print(a", "b", "x", "y)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Cino Hilliard, Sep 10 2006
EXTENSIONS
Name and Data corrected by Robert Israel, Aug 02 2018
STATUS
approved