Problems & Puzzles:
Some more terms
Maybe some of your puzzlers can find some
more terms of the following three nice sequences:
Contributions came from J. K. Andersen & Giovanni
Andersen wrote (6/5/07):
A090872(6) is 2072005925466, since these are primes:
The solution can also be added to puzzle 137. Yves Gallot's estimate
of 10^14 in puzzle 137 was too high.
Giovanni wrote (11/5/07)
the next term of
A090872 = a(n), is the smallest number m greater than 1
such that m^2^k+1 for k=0,1,...,n are primes is 2072005925466. I
stopped my search there.
I've searched also for
A090875 = a(n) is the smallest number m such that m^(2^k)
+ 2^(2^k) is prime for k=0,1,...,n. up to 2,365,100,000,000 but I
did not find the next term.