OFFSET
1,1
COMMENTS
The definition is similar to Fortunate numbers (A005235) but uses 2^n instead of primorial A002110(n).
Terms a(n) are often but not always prime; sometimes they are prime powers or semiprimes or have a more general form.
An analog of Fortune's conjecture for this sequence would be "a(n) is either a prime power or a semiprime." But even this relaxed conjecture is disproved by, e.g., a(62)=135, a(93)=a(97)=105, a(99)=255.
By definition, a(n) >= A013597(n). The integers n such that a(n) > A013597(n) are those with A013597(n)=1, i.e., 1, 2, 4, 8, 16, and then? - Michel Marcus, Nov 06 2015
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..2000
EXAMPLE
a(56)=81 because m=81 is the least m > 1 such that m + 2^56 is prime.
MATHEMATICA
Table[m = 2; While[! PrimeQ[m + 2^n], m++]; m, {n, 75}] (* Michael De Vlieger, Nov 06 2015 *)
PROG
(PARI) a(n)=my(m=2); while(!isprime(m+2^n), m++); m \\ Anders Hellström, Nov 02 2015
(PARI) a(n)=nextprime(2^n+2)-2^n \\ Charles R Greathouse IV, Nov 02 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexei Kourbatov, Nov 02 2015
EXTENSIONS
a(60) corrected by Charles R Greathouse IV, Nov 02 2015
STATUS
approved