A057755 Number of digits in n-th Fermat number (A000215).

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

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