|
%I #25 Apr 11 2020 06:11:21
%S 16661,1103,1417831,1143749,14282381,11699423,1950071,7503425119,
%T 3837692792387,145857793,76607717987,1755833757671518620617,
%U 17416012536871141,1000000000000066600000000000001,16540928199996367,744657085412168192717253704669
%N Largest prime factor of the Belphegor number B(n) = (10^(n+3) + 666)*10^(n+1) + 1.
%C The Belphegor numbers (A232449), though not often prime themselves (see A232448), tend to contain very large prime factors and are therefore hard to factorize.
%H Stanislav Sykora and Amiram Eldar, <a href="/A232450/b232450.txt">Table of n, a(n) for n = 0..64</a> (terms 0..44 from Stanislav Sykora)
%H Clifford A. Pickover, <a href="http://sprott.physics.wisc.edu/pickover/pc/1000000000000066600000000000001.html">Belphegor's Prime: 1000000000000066600000000000001</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Belphegor%27s_Prime">Belphegor's prime</a>
%t Table[FactorInteger[(10^(n + 3) + 666)*10^(n + 1) + 1][[-1, 1]], {n, 20}] (* _T. D. Noe_, Nov 25 2013 *)
%o (PARI) default(factor_proven,1);
%o Belphegor(k)=(10^(k+3)+666)*10^(k+1)+1;
%o LargestPrimeFactor(k)={local(f);f=factor(k);return(f[#f[,1],1])};
%o nmax=40; v=vector(nmax);
%o for (n=0,#v-1,v[n+1]=LargestPrimeFactor(Belphegor(n));print(v[n+1]))
%Y Cf. A232448 (indices of Belphegor primes), A232449 (Belphegor numbers).
%K nonn
%O 0,1
%A _Stanislav Sykora_, Nov 24 2013
| 