OFFSET
0,3
COMMENTS
The smallest known prime factors of 10^(2^15)+1 to 10^(2^18)+1 are 65537, 8257537, 175636481, 639631361. - Jeppe Stig Nielsen, Nov 04 2010
Above values for a(15)-a(18) are confirmed. a(19) = 70254593, a(20) = 167772161. - Chai Wah Wu, Oct 16 2019
a(14) <= 1702047085242613845984907230501142529. - Max Alekseyev, Feb 26 2023
LINKS
factordb.com, Status of 10^(2^n)+1.
FORMULA
If 10^(2^n)+1 is composite, a(n) = A185121(n).
EXAMPLE
10^(2^4)+1 = 10000000000000001 = 353*449*641*1409*69857, hence a(4) = 353.
MATHEMATICA
spf[n_]:=Module[{c=10^2^n+1}, If[PrimeQ[c], 1, FactorInteger[c][[1, 1]]]]; Array[spf, 15, 0] (* Harvey P. Dale, Apr 09 2019 *)
PROG
(PARI) for(k=0, 8, fac=factor(10^(2^k)+1); print1(if(matsize(fac)[1]==1, 1, fac[1, 1]), ", "))
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004
EXTENSIONS
a(13) from the Keller link, added by Jeppe Stig Nielsen, Nov 04 2010
STATUS
approved