A102050 a(n) = 1 if 10^(2^n)+1 is prime, otherwise smallest prime factor of 10^(2^n)+1.

1, 1, 73, 17, 353, 19841, 1265011073, 257, 10753, 1514497, 1856104284667693057, 106907803649, 458924033, 3635898263938497962802538435084289

Offset: 0

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

Keywords

• nonn
• hard
• more

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

Examples

			10^(2^4)+1 = 10000000000000001 = 353*449*641*1409*69857, hence a(4) = 353.
		

Links

• factordb.com, Status of 10^(2^n)+1.
• Wilfrid Keller, Prime factors of generalized Fermat numbers Fm(10) and complete factoring status

Crossrefs

Cf. A000533, A002275, A062397.

Programs

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 *)

PARI

for(k=0,8,fac=factor(10^(2^k)+1);print1(if(matsize(fac)[1]==1,1,fac[1,1]),","))

Formula

If 10^(2^n)+1 is composite, a(n) = A185121(n).

Extensions

a(13) from the Keller link, added by Jeppe Stig Nielsen, Nov 04 2010