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%I #39 Sep 08 2022 08:45:02
%S 1,1,2,3,5,10,20,39,78,155,309,617,1234,2467,4933,9865,19729,39457,
%T 78914,157827,315653,631306,1262612,2525223,5050446,10100891,20201782,
%U 40403563,80807125,161614249,323228497,646456994,1292913987,2585827973
%N Number of digits in n-th Fermat number (A000215).
%C Also number of digits of A001146(n) and A051179(n). - _Michel Marcus_, Dec 21 2018
%D John H. Conway and R. K. Guy, The Book of Numbers, Copernicus, an imprint of Springer-Verlag, NY, 1995, page 139.
%H Vincenzo Librandi, <a href="/A057755/b057755.txt">Table of n, a(n) for n = 0..1000</a> (first 100 terms from Jinyuan Wang)
%H R. Mestrovic, <a href="http://arxiv.org/abs/1202.3670">Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof</a>, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2018. - From _N. J. A. Sloane_, Jun 13 2012
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FermatNumber.html">Fermat Number</a>
%F a(n) = floor(log_10(F_n)+1) (F_n is the n-th Fermat number). - _Ivan Panchenko_, Sep 06 2009
%e a(6) = 20 because 2^(2^6) + 1 = 18446744073709551617 which is a twenty-digit number.
%p seq(length(2^(2^n)),n=0..20); # _Zerinvary Lajos_, Apr 20 2008
%t Table[ Floor[ 2^n * N[ Log[ 10, 2 ], 24 ] + 1 ], {n, 0, 43} ]
%o (PARI) for(n=0, 50, print(n, " ", floor(2^n*log(2)/log(10))+1); ) \\ _Jinyuan Wang_, Nov 07 2018
%o (Magma) [Floor(2^n*Log(10,2)/Log(10,10))+1: n in [0..40]]; // _Vincenzo Librandi_, Nov 08 2018
%o (GAP) List([0..18],n->Size(ListOfDigits(2^(2^n)+1))); # _Muniru A Asiru_, Dec 20 2018
%Y Cf. A000215, A001146, A051179.
%K nonn,base
%O 0,3
%A _Robert G. Wilson v_, Oct 30 2000
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