|
Search: id:A102050
|
|
|
| A102050 |
|
a(n) = 1 if 10^(2^n)+1 is prime, otherwise smallest prime factor of 10^(2^n)+1. |
|
+0
2
|
|
| 1, 1, 73, 17, 353, 19841, 1265011073, 257, 10753, 1514497, 1856104284667693057, 106907803649, 458924033
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
10^(2^13)+1 and 10^(2^14)+1 are composite, but no prime factors are known. The smallest known prime factors of 10^(2^15)+1 to 10^(2^18)+1 are 65537, 8257537, 175636481, 639631361.
|
|
LINKS
|
Wilfrid Keller, Prime factors of generalized Fermat numbers Fm(10) and complete factoring status
|
|
EXAMPLE
|
10^(2^4)+1 = 10000000000000001 = 353*449*641*1409*69857, hence a(4) = 353.
|
|
PROGRAM
|
(PARI) for(k=0, 8, fac=factor(10^(2^k)+1); print1(if(matsize(fac)[1]==1, 1, fac[1, 1]), ", "))
|
|
CROSSREFS
|
Cf. A000533, A002275.
Sequence in context: A113889 A099191 A051325 this_sequence A057446 A033393 A064667
Adjacent sequences: A102047 A102048 A102049 this_sequence A102051 A102052 A102053
|
|
KEYWORD
|
nonn,hard,more
|
|
AUTHOR
|
Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004
|
|
|
Search completed in 0.002 seconds
|
