OFFSET
1,1
COMMENTS
From Gord Palameta, Jul 19 2018: (Start)
All terms after the first two are congruent to 1 modulo 4, because if p is a Sophie Germain prime that is congruent to 3 modulo 4 then 2p + 1 divides 2^p - 1.
Boklan and Conway conjecture that this sequence is finite.
(End)
LINKS
David W. Ash, Ian F. Blake, and Scott A. Vanstone, Low Complexity Normal Bases, Discrete Applied Mathematics, 25(1989), 206.
Kent D. Boklan, John H. Conway, Expect at most one billionth of a new Fermat Prime!, arXiv:1605.01371 [math.NT], 2016, p. 6.
EXAMPLE
31 = 2^5 - 1 and 11 = 2 * 5 + 1 are primes.
MATHEMATICA
Select[Prime[Range[1000]], PrimeQ[2# + 1] && PrimeQ[2^# - 1] &] (* Alonso del Arte, Jul 20 2018 *)
Select[Prime@ Range[10^6], And[PrimeQ[2 # + 1], MersennePrimeExponentQ@ #] &] (* Michael De Vlieger, Jul 20 2018 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Labos Elemer, Nov 06 2001
EXTENSIONS
a(8) = 43112609, since the ordinal position of this term in A000043 is now confirmed. - Gord Palameta, Jul 19 2018
STATUS
approved