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A352736
a(n) is the smallest b >= 2 such that 1 + Sum_{k=0..n} b^(2^k) is prime, or 1 if no such b exists.
0
2, 2, 2, 1, 6, 3, 448, 107, 104, 1, 4556, 1, 24124, 121209, 368, 177817, 48330, 1
OFFSET
0,1
COMMENTS
Polynomial factorizations exist for n=3,9,11,17,27 and may exist for other n > 27.
For those n for which a proven factorization exists, b=1 results in a prime of the form n+2.
EXAMPLE
a(6)=448 because 448 is the smallest number b such that 1 + Sum_{k=0..6} b^(2^k) is prime.
CROSSREFS
Sequence in context: A285183 A255399 A181830 * A086612 A128207 A340740
KEYWORD
nonn,hard,more
AUTHOR
Kellen Shenton, Mar 30 2022
EXTENSIONS
a(16)-a(17) from Kellen Shenton, May 08 2022
STATUS
approved