login
A232450
Largest prime factor of the Belphegor number B(n) = (10^(n+3) + 666)*10^(n+1) + 1.
4
16661, 1103, 1417831, 1143749, 14282381, 11699423, 1950071, 7503425119, 3837692792387, 145857793, 76607717987, 1755833757671518620617, 17416012536871141, 1000000000000066600000000000001, 16540928199996367, 744657085412168192717253704669
OFFSET
0,1
COMMENTS
The Belphegor numbers (A232449), though not often prime themselves (see A232448), tend to contain very large prime factors and are therefore hard to factorize.
LINKS
Stanislav Sykora and Amiram Eldar, Table of n, a(n) for n = 0..64 (terms 0..44 from Stanislav Sykora)
MATHEMATICA
Table[FactorInteger[(10^(n + 3) + 666)*10^(n + 1) + 1][[-1, 1]], {n, 20}] (* T. D. Noe, Nov 25 2013 *)
PROG
(PARI) default(factor_proven, 1);
Belphegor(k)=(10^(k+3)+666)*10^(k+1)+1;
LargestPrimeFactor(k)={local(f); f=factor(k); return(f[#f[, 1], 1])};
nmax=40; v=vector(nmax);
for (n=0, #v-1, v[n+1]=LargestPrimeFactor(Belphegor(n)); print(v[n+1]))
CROSSREFS
Cf. A232448 (indices of Belphegor primes), A232449 (Belphegor numbers).
Sequence in context: A170788 A057329 A349773 * A317179 A196023 A108843
KEYWORD
nonn
AUTHOR
Stanislav Sykora, Nov 24 2013
STATUS
approved