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 A080176 Generalized Fermat numbers: 10^(2^n) + 1, n >= 0. 13
 11, 101, 10001, 100000001, 10000000000000001, 100000000000000000000000000000001, 10000000000000000000000000000000000000000000000000000000000000001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS As for standard Fermat numbers 2^(2^n) + 1, a number (2b)^m + 1 (with b > 1) can only be prime if m is a power of 2. On the other hand, out of the first 12 base-10 Fermat numbers, only the first two are primes. Also, binary representation of Fermat numbers (in decimal, see A000215). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..9 (shortened by N. J. A. Sloane, Jan 13 2019) Anders Björn and Hans Riesel, Factors of Generalized Fermat Numbers, Mathematics of Computation, Vol. 67, No. 221, Jan., 1998, pp. 441-446. C. K. Caldwell, "Top Twenty" page, Generalized Fermat Divisors (base=10) Wilfrid Keller, GFN10 factoring status R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670, 2012 - From N. J. A. Sloane, Jun 13 2012 Eric Weisstein's World of Mathematics, Generalized Fermat Number OEIS Wiki, Generalized Fermat numbers FORMULA a(0) = 11; a(n) = (a(n - 1) - 1)^2 + 1. a(n) = 9*a(n-1)*a(n-2)*...*a(1)*a(0) + 2, n >= 0, where for n = 0, we get 9*(empty product, i.e., 1)+ 2 = 11 = a(0). - Daniel Forgues, Jun 20 2011 EXAMPLE a(0) = 10^1 + 1 = 11 = 9*(1) + 2 = 9*(empty product) + 2. a(1) = 10^2 + 1 = 101 = 9*(11) + 2. a(2) = 10^4 + 1 = 10001 = 9*(11*101) + 2. a(3) = 10^8 + 1 = 100000001 = 9*(11*101*10001) + 2. a(4) = 10^16 + 1 = 10000000000000001 = 9*(11*101*10001*100000001) + 2. a(5) = 10^32 + 1 = 100000000000000000000000000000001 = 9*(11*101*10001*100000001*10000000000000001) + 2. MATHEMATICA Table[10^2^n + 1, {n, 0, 6}] (* Arkadiusz Wesolowski, Nov 02 2012 *) PROG (MAGMA) [10^(2^n) + 1: n in [0..8]]; // Vincenzo Librandi, Jun 20 2011 CROSSREFS Cf. A000215 Fermat numbers: 2^(2^n) + 1, n >= 0. Cf. A019434, A080174, A080175, A059919, A199591, A078303, A078304, A152581, A199592, A152585. Sequence in context: A070854 A075767 A292014 * A064490 A080439 A098153 Adjacent sequences:  A080173 A080174 A080175 * A080177 A080178 A080179 KEYWORD easy,nonn AUTHOR Jens Voß, Feb 04 2003 EXTENSIONS Edited by Daniel Forgues, Jun 19 2011 STATUS approved

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Last modified September 17 13:00 EDT 2019. Contains 327131 sequences. (Running on oeis4.)