|
| |
|
|
A059917
|
|
a(n) = (3^(2^n)+1)/2 = A059919(n)/2, n >= 0.
|
|
4
| | |
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| Average of first 2^(n+1) powers of 3 divided by average of first 2^n powers of 3.
Numerator of b(n) where b(n) = 1/2*(b(n-1) + 1/b(n-1)), b(0)=2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 15 2002
From Daniel Forgues, Jun 22 2011: (Start)
Since for the generalized Fermat numbers 3^(2^n)+1 (A059919), we have a(n) = 2*a(n-1)*a(n-2)*...*a(1)*a(0) + 2, n >= 0, where for n = 0, we get 2*(empty product, i.e. 1)+ 2 = 4 = a(0). This formula implies that the GCD of any pair of terms of A059919 is 2, which means that the terms of (3^(2^n)+1)/2 (A059917) are pairwise coprime.
2, 5, 41, 21523361, 926510094425921 are prime. 3281 = 17*193. (End)
|
|
|
LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,11
|
|
|
FORMULA
| a(n) = a(n-1)*(3^(2^(n-1))+1)-3^(2^(n-1)) = A059723(n+1)/A059723(n) = A059918(n)+1 = a(n-1)*A059919(n-1)-A011764(n-1)
a(0) = 2; a(n) = ((2*a(n-1) - 1)^2 + 1)/2, n >= 1. - Daniel Forgues, Jun 22 2011
|
|
|
EXAMPLE
| a(2) = Average(1,3,9,27,81,243,729,2187)/Average(1,3,9,27) = 410/10 = 41
|
|
|
PROG
| (PARI) { for (n=0, 11, write("b059917.txt", n, " ", (3^(2^n) + 1)/2); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 30 2009]
|
|
|
CROSSREFS
| Cf. A059918, A059919.
Sequence in context: A126469 A054859 A076725 * A093625 A042447 A176266
Adjacent sequences: A059914 A059915 A059916 * A059918 A059919 A059920
|
|
|
KEYWORD
| nonn,frac
|
|
|
AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Feb 08 2001
|
| |
|
|
