

A052007


Numbers m such that 2^m + m is prime.


13



1, 3, 5, 9, 15, 39, 75, 81, 89, 317, 701, 735, 1311, 1881, 3201, 3225, 11795, 88071, 204129, 678561
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OFFSET

1,2


COMMENTS

Terms >= 701 are currently only strong pseudoprimes.
If m=1 (mod 6) or m=2 (mod 6) then 3 divides 2^m+m. Thus for n > 1, a(n)!=1 (mod 6) and a(n)!=2 (mod 6).
Some of the results were computed using the PrimeFormGW (PFGW) primalitytesting program.  Hugo Pfoertner, Nov 14 2019
Keller (see Links) notes that a Mersenne number M(2^m+m) = 2^(2^m+m)  1 can be written as (2^m)*2^(2^m)  1, and lists the first twelve terms of this sequence. The last known case where M(2^m+m) is prime is for m=a(4)=9, which gives the prime M(521).  Jeppe Stig Nielsen, Apr 20 2021


LINKS



EXAMPLE

2^39 + 39 = 549755813927 is prime.


MATHEMATICA

Do[ If[ PrimeQ[ 2^n + n ], Print[ n ] ], {n, 0, 7000} ]
v={1}; Do[If[Mod[n, 2]*(Mod[n, 6]1)!= 0&&PrimeQ[2^n+n], v=Append[v, n]; Print[v]], {n, 2, 20000}]


PROG



CROSSREFS



KEYWORD

nonn,nice,hard,more


AUTHOR



EXTENSIONS



STATUS

approved



