OFFSET
1,1
COMMENTS
Consecutive prime powers with positive exponents.
a(n) = Ordered union of {2^3, 3^2, Fermat primes, Fermat primes - 1, Mersenne primes, Mersenne primes + 1}.
It is not known whether this sequence is infinite (but it is believed to be).
2^3, 3^2 are the only consecutive prime powers with exponents >= 2 (this is a consequence of the Catalan-Mihailescu theorem).
Only the first 5 Fermat numbers f_0 to f_4 are known to be prime.
It is conjectured that there exist an infinite number of Mersenne primes.
LINKS
Daniel Forgues, Table of n, a(n) for n = 1..48
Eric Weisstein's World of Mathematics, Catalan's Conjecture.
Eric Weisstein's World of Mathematics, Mersenne Prime.
Eric Weisstein's World of Mathematics, Fermat Prime.
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
Daniel Forgues, Aug 14 2009
EXTENSIONS
Edited by N. J. A. Sloane, Aug 24 2009
STATUS
approved