OFFSET
0,1
COMMENTS
k = 44745755^4 has the property that k + 2^m is composite for all m. However, it is conjectured that this sequence is unbounded. This is the case if and only if A336347 is unbounded; because a full covering set for k*2^m + 1 would also be a full covering for k + 2^m, and vice versa.
LINKS
Jeppe Stig Nielsen, Table of n, a(n) for n = 0..500
M. Filaseta et al., On powers associated with Sierpiński numbers, Riesel numbers and Polignac's conjecture, Journal of Number Theory, Volume 128, Issue 7 (July 2008), pp. 1916-1940.
Anatoly S. Izotov, A Note on Sierpinski Numbers, Fibonacci Quarterly (1995), pp. 206-207.
PROG
(PARI) a(n) = vecmin(factor(44745755^4+2^(4*n+2))[, 1]); \\ Michel Marcus, Aug 08 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeppe Stig Nielsen, Aug 08 2020
STATUS
approved