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%I #31 Jul 08 2023 10:43:02
%S 316912650057057350374175801344000001
%N Smallest prime factor of Googolplex + n which exceeds 16.
%C a(2) is not known. After a(1) the sequence continues ?, 1429, 1129, 29, ?, 53, 427169, 5501, 19, 59, 1327, 1645318771, 61, 211, 17, 1831, ?, 43, 389, 173, 233886337, 139, 1451, 18797, 31, 37, 8297, 19, 13879, ?, 9241, 17, 29, ...
%C The question marks indicate terms > 10^14. - _Dario Alpern_, May 17 2003
%H Tanya Khovanova, <a href="https://www.tanyakhovanova.com/RecursiveSequences/NonRecursions.html">Non Recursions</a>
%H Dario Alejandro Alpern, <a href="https://www.alpertron.com.ar/GOOGOL.HTM">Factors of 1000 numbers starting from googolplex</a>
%H Robert Harley, <a href="https://pauillac.inria.fr/~harley/bits.html">Factors of Googolplex+1</a> (Found some terms)
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Googolplex.html">Googolplex</a>
%H <a href="/index/O#oneterm">Index entries for one-term sequences</a>
%t (* For any individual n *) k = 17; While[ !PrimeQ[k] || PowerMod[10, 10^100, k] + n != k, k += 2]; k
%Y Cf. A078814.
%K hard,nonn,bref,more,less
%O 1,1
%A _Ed Pegg Jr_ and _Robert G. Wilson v_, Nov 21 2002