OFFSET
1,1
COMMENTS
Clearly each term is congruent to 1 modulo 6.
By the conjecture in A234309, this sequence should have infinitely many terms.
Note that any Mersenne prime greater than 3 has the form 2^{2*k+1} - 1 = 4^k + 4^k - 1, where k is a positive integer.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..800
EXAMPLE
a(1) = 7 since 7 = 4^1 + 4^1 - 1 is prime.
a(2) = 19 since 19 = 4^1 + 4^2 - 1 is prime.
a(3) = 31 since 31 = 4^2 + 4^2 - 1 is prime.
MATHEMATICA
n=0; Do[If[PrimeQ[4^k+4^m-1], n=n+1; Print[n, " ", 4^m+4^k-1]], {m, 1, 250}, {k, 1, m}]
PROG
(PARI) for(k=1, 30, for(m=1, k, if(ispseudoprime(t=4^k+4^m-1), print1(t", ")))) \\ Charles R Greathouse IV, Dec 23 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Dec 23 2013
STATUS
approved