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A336347
Least prime factor of 44745755^4*2^(4n+2) + 1.
2
13, 101, 29, 13, 39877, 41, 13, 37, 18661, 13, 41, 73, 13, 5719237, 144341, 13, 29, 89, 13, 353, 41, 13, 64450569241, 29, 13, 37, 101, 13, 89, 53, 13, 113, 313, 13, 37, 41, 13, 29, 73, 13, 41, 181, 13, 37, 29, 13, 857, 73, 13, 389, 41, 13, 37
OFFSET
0,1
COMMENTS
There are k such that k*2^m + 1 is not prime for any m (then k is called a Sierpiński number). Erdős once conjectured that for such a k, the smallest prime factor of k*2^m + 1 would be bounded as m tends to infinitiy. The proven Sierpiński number k=44745755^4 is thought to be the first counterexample to this conjecture.
This sequence is either unbounded (in which case 44745755^4 is in fact a counterexample) or periodic.
a(229) <= 3034663491871541. - Chai Wah Wu, Aug 09 2020
LINKS
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeppe Stig Nielsen, Jul 19 2020
STATUS
approved