Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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