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%I #32 Feb 26 2023 20:14:06
%S 1,1,73,17,353,19841,1265011073,257,10753,1514497,1856104284667693057,
%T 106907803649,458924033,3635898263938497962802538435084289
%N a(n) = 1 if 10^(2^n)+1 is prime, otherwise smallest prime factor of 10^(2^n)+1.
%C 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
%C Above values for a(15)-a(18) are confirmed. a(19) = 70254593, a(20) = 167772161. - _Chai Wah Wu_, Oct 16 2019
%C a(14) <= 1702047085242613845984907230501142529. - _Max Alekseyev_, Feb 26 2023
%H factordb.com, <a href="http://factordb.com/index.php?query=10%5E%282%5En%29%2B1">Status of 10^(2^n)+1</a>.
%H Wilfrid Keller, <a href="http://www.prothsearch.com/GFN10.html">Prime factors of generalized Fermat numbers Fm(10) and complete factoring status</a>
%F If 10^(2^n)+1 is composite, a(n) = A185121(n).
%e 10^(2^4)+1 = 10000000000000001 = 353*449*641*1409*69857, hence a(4) = 353.
%t 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 *)
%o (PARI) for(k=0,8,fac=factor(10^(2^k)+1);print1(if(matsize(fac)[1]==1,1,fac[1,1]),","))
%Y Cf. A000533, A002275, A062397.
%K nonn,hard,more
%O 0,3
%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004
%E a(13) from the Keller link, added by _Jeppe Stig Nielsen_, Nov 04 2010
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