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 A185121 Smallest prime factor of 10^(2^n) + 1. 7
 11, 101, 73, 17, 353, 19841, 1265011073, 257, 10753, 1514497, 1856104284667693057, 106907803649, 458924033, 3635898263938497962802538435084289 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 10^k+1 can only be prime if k is a power of 2. So far the only known primes of this form are a(0) = 11 and a(1) = 101. [Edited by M. F. Hasler, Aug 03 2019] a(n) >= 2^(n+1)+1; we have a(n) = 2^(n+1)+1 for n=3, n=7, and n=15. a(14) > 10^16. - Max Alekseyev, Jun 28 2013 From the Keller link a(15)-a(20) = 65537, 8257537, 175636481, 639631361, 70254593, 167772161. - Ray Chandler, Dec 27 2013 LINKS Table of n, a(n) for n=0..13. FactorDB, Factorizations of 10^(2^n)+1 Makoto Kamada, Factorizations of 100...001 Wilfrid Keller, Prime factors of generalized Fermat numbers Fm(10) and complete factoring status FORMULA a(n) = A038371(2^n). - M. F. Hasler, Jul 30 2019 EXAMPLE For n=2, a(2)=73 since 10^(2^2) + 1 = 10001 = 73 * 137. MATHEMATICA Table[With[{k = 2^n}, FactorInteger[10^k + 1]][[1, 1]], {n, 0, 13, 1}] (* Vincenzo Librandi, Jul 23 2013 *) PROG (PARI) a(n) = factor(10^(2^n)+1)[1, 1] \\ Michel Marcus, May 30 2013 CROSSREFS Cf. A038371, A000533, A000215, A093179, A102050 Essentially the same as A102050. - Sean A. Irvine, Feb 17 2013 Sequence in context: A330290 A330291 A318647 * A133835 A326108 A292451 Adjacent sequences: A185118 A185119 A185120 * A185122 A185123 A185124 KEYWORD nonn,more,hard AUTHOR Sergio Pimentel, Jan 22 2012 STATUS approved

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Last modified December 10 04:38 EST 2023. Contains 367699 sequences. (Running on oeis4.)