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%I #13 Aug 09 2020 15:32:01
%S 797,37,13,113,29,13,73,2593,13,41,37,13,509,57881,13,73,293,13,29,37,
%T 13,7555049,53,13,41,29,13,677,37,13,8557781,113,13,73,41,13,397,37,
%U 13,29,1217,13,73,9820301,13,113,29,13,53,41,13,73,113,13,41,37,13
%N Least prime factor of 44745755^4 + 2^(4n+2).
%C 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.
%H Jeppe Stig Nielsen, <a href="/A336943/b336943.txt">Table of n, a(n) for n = 0..500</a>
%H M. Filaseta et al., <a href="https://doi.org/10.1016/j.jnt.2008.02.004">On powers associated with Sierpiński numbers, Riesel numbers and Polignac's conjecture</a>, Journal of Number Theory, Volume 128, Issue 7 (July 2008), pp. 1916-1940.
%H Anatoly S. Izotov, <a href="https://www.fq.math.ca/Scanned/33-3/izotov.pdf">A Note on Sierpinski Numbers</a>, Fibonacci Quarterly (1995), pp. 206-207.
%o (PARI) a(n) = vecmin(factor(44745755^4+2^(4*n+2))[,1]); \\ _Michel Marcus_, Aug 08 2020
%Y Cf. A020639, A076336, A213353, A336347.
%K nonn
%O 0,1
%A _Jeppe Stig Nielsen_, Aug 08 2020
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