OFFSET
0,3
COMMENTS
REFERENCES
John H. Conway and R. K. Guy, The Book of Numbers, Copernicus, an imprint of Springer-Verlag, NY, 1995, page 139.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000 (first 100 terms from Jinyuan Wang)
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 [math.HO], 2012-2018. - From N. J. A. Sloane, Jun 13 2012
Eric Weisstein's World of Mathematics, Fermat Number
FORMULA
a(n) = floor(log_10(F_n)+1) (F_n is the n-th Fermat number). - Ivan Panchenko, Sep 06 2009
EXAMPLE
a(6) = 20 because 2^(2^6) + 1 = 18446744073709551617 which is a twenty-digit number.
MAPLE
seq(length(2^(2^n)), n=0..20); # Zerinvary Lajos, Apr 20 2008
MATHEMATICA
Table[ Floor[ 2^n * N[ Log[ 10, 2 ], 24 ] + 1 ], {n, 0, 43} ]
PROG
(PARI) for(n=0, 50, print(n, " ", floor(2^n*log(2)/log(10))+1); ) \\ Jinyuan Wang, Nov 07 2018
(Magma) [Floor(2^n*Log(10, 2)/Log(10, 10))+1: n in [0..40]]; // Vincenzo Librandi, Nov 08 2018
(GAP) List([0..18], n->Size(ListOfDigits(2^(2^n)+1))); # Muniru A Asiru, Dec 20 2018
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Robert G. Wilson v, Oct 30 2000
STATUS
approved