OFFSET
1,1
COMMENTS
The next term is too large to include.
Numbers (2^n - 1)*2^(n - 1) such that both 2^n - 1 and 2^n + 2*n - 3 are prime.
Conjectures (defining x = 170141183460469231731687303715884105727 = A007013(4)}:
(1) (2^x - 1)*2^(x - 1) is a term because 2^x - 1 and 2^x + 2*x - 3 are primes;
EXAMPLE
a(1) = (2^2-1)*2^(2-1) = 6 because both 2^2-1 = 3 and 2^2+2*2-3 = 5 are primes.
a(2) = (2^3-1)*2^(3-1) = 28 because both 2^3-1 = 7 and 2^3+2*3-3 = 11 are primes.
a(3) = (2^7-1)*2^(7-1) = 8128 because both 2^7-1 = 127 and 2^7+2*7-3 = 139 are primes.
MAPLE
A276493:=n->`if`(isprime(n) and isprime(2^n-1) and isprime(2^n+2*n-3), (2^n-1)*2^(n-1), NULL): seq(A276493(n), n=1..10^3); # Wesley Ivan Hurt, Sep 07 2016
MATHEMATICA
Select[PerfectNumber[Range[12]], PrimeQ[Total[Flatten[Table[#[[1]], #[[2]]]&/@ FactorInteger[#]]]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 06 2020 *)
PROG
(Magma) [(2^p-1)*2^(p-1): p in PrimesUpTo(2000) | IsPrime(2^p+2*p-3)];
(Magma) [(2^n-1)*2^(n-1): n in [1..200] | IsPrime(n) and IsPrime(2^n-1) and IsPrime(2^n+2*n-3)]; // Vincenzo Librandi, Sep 06 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Juri-Stepan Gerasimov, Sep 05 2016
STATUS
approved