A181355 a(3*n+1) = 4^(2^n), a(3*n+2) = 3^(2^n), a(3*n+3) = 4^(2^n) - 3^(2^n).

4, 3, 1, 16, 9, 7, 256, 81, 175, 65536, 6561, 58975, 4294967296, 43046721, 4251920575, 18446744073709551616, 1853020188851841, 18444891053520699775, 340282366920938463463374607431768211456, 3433683820292512484657849089281

Offset

1,1

Comments

Previous name was: Consider pairs of fractions (x,y) starting (4,3) and updated via z:=1/(1/x+1/y), x->x-z, y->y-z. The sequence shows the triples (numerator(x), numerator(y), numerator(x)-numerator(y)) after each update.

Links

Table of n, a(n) for n=1..20.

Formula

a(3*n+1) = 4^(2^n), a(3*n+2) = 3^(2^n), a(3*n+3) = 4^(2^n) - 3^(2^n). - Philippe Deléham , Oct 29 2013

Example

(x=4,y=3) is shown as the first triple (4,3,1) in the sequence. This generates z=12/7 which generates the new pair (x,y) = (16/7,9/7) shown as (16,9,7). - R. J. Mathar, Feb 09 2011

Maple

x := 4 ; y := 3 ;
for loo from 1 to 7 do printf("%d, %d, %d, ", numer(x), numer(y), numer(x)-numer(y)) ; z := 1/(1/x+1/y) ; x := x-z ; y := y-z ; end do: # R. J. Mathar, Feb 09 2011

Crossrefs

Sequence in context: A308326 A098234 A193795 * A128320 A189507 A348436

Adjacent sequences: A181352 A181353 A181354 * A181356 A181357 A181358

Keyword

nonn,easy,less

Author

Jamel Ghanouchi, Jan 27 2011

Extensions

Corrected by Philippe Deléham, Oct 29 2013

New name using Philippe Deléham's formula, Joerg Arndt, Nov 14 2014

Status

approved