OFFSET
1,3
COMMENTS
Equivalently, smallest k such that k*n + 1 is a Mersenne exponent (A000043).
As of Mar 11 2017, the j-th Mersenne exponent A000043(j) is known for j=1..45; four additional terms of A000043 are listed in the Extensions for that sequence, but it is not yet known whether they are A000043(46) through A000043(49). None of the first 45 Mersenne exponents are of the form k*29 + 1, so a(29) > floor((A000043(45) - 1)/29) = floor((37156667 - 1)/29) = 1281264. However, one of the four additional terms is 57885161 = 1996040*29 + 1; thus, 1281264 < a(29) <= 1996040.
a(39) > floor((A000043(45) - 1)/39) = 952735.
EXAMPLE
a(1) = 1 because sigma(2^(1*1)) = sigma(2) = 1 + 2 = 3 is prime. (1*1 + 1 = 2 = A000043(1).)
PROG
(PARI) a(n) = k=1; while(!isprime(sigma(2^(k*n))), k++); k; \\ Michel Marcus, Mar 12 2017
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Jon E. Schoenfield, Mar 11 2017
EXTENSIONS
a(29)-a(38) from Jinyuan Wang, Mar 25 2023
STATUS
approved