A336943 Least prime factor of 44745755^4 + 2^(4n+2).

797, 37, 13, 113, 29, 13, 73, 2593, 13, 41, 37, 13, 509, 57881, 13, 73, 293, 13, 29, 37, 13, 7555049, 53, 13, 41, 29, 13, 677, 37, 13, 8557781, 113, 13, 73, 41, 13, 397, 37, 13, 29, 1217, 13, 73, 9820301, 13, 113, 29, 13, 53, 41, 13, 73, 113, 13, 41, 37, 13

Offset: 0

Author

Jeppe Stig Nielsen, Aug 08 2020

Keywords

• nonn

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.

Crossrefs

Cf. A020639, A076336, A213353, A336347.

Programs

PARI

a(n) = vecmin(factor(44745755^4+2^(4*n+2))[,1]); \\ Michel Marcus, Aug 08 2020