A336347 Least prime factor of 44745755^4*2^(4n+2) + 1.

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

Author

Jeppe Stig Nielsen, Jul 19 2020

Keywords

• nonn

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

• Jeppe Stig Nielsen, Table of n, a(n) for n = 0..228
• 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

Cf. A020639, A076336, A213353, A258091, A336943.