A232450 Largest prime factor of the Belphegor number B(n) = (10^(n+3) + 666)*10^(n+1) + 1.

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)

Clifford A. Pickover, Belphegor's Prime: 1000000000000066600000000000001

Wikipedia, Belphegor's prime

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

Adjacent sequences: A232447 A232448 A232449 * A232451 A232452 A232453

Keyword

nonn

Author

Stanislav Sykora, Nov 24 2013

Status

approved