OFFSET
1,1
COMMENTS
We have the polynomial factorization: n^10+1 = (n^2+1) * (n^8 - n^6 + n^4 - n^2 + 1) Hence after the initial n=1 prime the binomial can only be semiprime if n^2 + 1 is prime and n^8 - n^6 + n^4 - n^2 + 1 is prime.
LINKS
Robert Price, Table of n, a(n) for n = 1..1105
EXAMPLE
4^10+1 = 1048577 = 17 * 61681,
16^10+1 = 1099511627777 = 257 * 4278255361,
1010^10+1 = 1104622125411204510010000000001 = 1020101 * 1082855644108970101989901.
MATHEMATICA
Select[ Range[5000], PrimeQ[ #^2 + 1] && PrimeQ[(#^10 + 1)/(#^2 + 1)] &] (* Robert G. Wilson v, Apr 08 2005 *)
Select[Range[4700], PrimeOmega[#^10+1]==2&] (* Harvey P. Dale, Jan 13 2013 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Apr 06 2005
EXTENSIONS
More terms from Robert G. Wilson v, Apr 08 2005
STATUS
approved