OFFSET
1,1
COMMENTS
Let p be a prime in this sequence. Call q=2^p-1 and r=(2^p+1)/3. The new Mersenne conjecture implies that either q and r are both prime or both composite.
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, Section A3.
LINKS
Gord Palameta, Table of n, a(n) for n = 1..40
P. T. Bateman, J. L. Selfridge, and S. S. Wagstaff, Jr., The New Mersenne Conjecture, Amer. Math. Monthly 96, 125-128, 1989.
John Renze and Eric Weisstein's World of Mathematics, MathWorld: New Mersenne Prime Conjecture.
MATHEMATICA
nn=100; Union[Select[1+2^Range[16], PrimeQ], Select[ -1+2^Range[2nn], PrimeQ], Select[3+4^Range[nn], PrimeQ], Select[ -3+4^Range[nn], PrimeQ]]
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Sep 12 2006
STATUS
approved