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A057755
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Number of digits in n-th Fermat number (A000215).
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3
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1, 1, 2, 3, 5, 10, 20, 39, 78, 155, 309, 617, 1234, 2467, 4933, 9865, 19729, 39457, 78914, 157827, 315653, 631306, 1262612, 2525223, 5050446, 10100891, 20201782, 40403563, 80807125, 161614249, 323228497, 646456994, 1292913987, 2585827973
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OFFSET
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0,3
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COMMENTS
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REFERENCES
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John H. Conway and R. K. Guy, The Book of Numbers, Copernicus, an imprint of Springer-Verlag, NY, 1995, page 139.
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LINKS
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FORMULA
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a(n) = floor(log_10(F_n)+1) (F_n is the n-th Fermat number). -Ivan Panchenko,Sep 06 2009
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EXAMPLE
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a(6) = 20 because 2^(2^6) + 1 = 18446744073709551617 which is a twenty-digit number.
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MAPLE
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MATHEMATICA
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Table[ Floor[ 2^n * N[ Log[ 10, 2 ], 24 ] + 1 ], {n, 0, 43} ]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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