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A057755 Number of digits in n-th Fermat number (A000215). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also number of digits of A001146(n) and A051179(n). - Michel Marcus, Dec 21 2018

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

Cf. A000215, A001146, A051179.

Sequence in context: A105369 A047101 A251703 * A262482 A293323 A257113

Adjacent sequences:  A057752 A057753 A057754 * A057756 A057757 A057758

KEYWORD

nonn,base

AUTHOR

Robert G. Wilson v, Oct 30 2000

STATUS

approved

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Last modified October 23 14:54 EDT 2019. Contains 328345 sequences. (Running on oeis4.)