Question 1083934
<pre><b>
{{{2^11 = 2048}}}, 2048÷19 = {{{107&15/19}}}, 1st term = numerator = 15
{{{2^12 = 4096}}}, 4096÷19 = {{{215&11/19}}}, 2nd term = numerator = 11
{{{2^13 = 8192}}}, 8192÷19 = {{{431&3/19}}}, 3rd term = numerator = 3
{{{2^14 = 16384}}}, 16384÷19 = {{{862&6/19}}}, 4th term = numerator = 6
{{{2^15 = 32768}}}, 32768÷19 = {{{1724&12/19}}}, 5th term = numerator = 12
{{{2^16 = 65536}}}, 65536÷19 = {{{3449&5/19}}}, 6th term = numerator = 5
{{{2^17 = 131072}}}, 131072÷19 = {{{6898&10/19}}}, 7th term = numerator = 10
{{{2^18 = 262144}}}, 262144÷19 = {{{13797&1/19}}}, 8th term = numerator = 1
{{{2^19 = 524288}}}, 524288÷19 = {{{27594&2/19}}}, 9th term = numerator = 2
{{{2^20 = 1048576}}}, 1048576÷19 = {{{55188&4/19}}}, 10th term = numerator = 4
{{{2^21 = 2097152}}}, 2097152÷19 = {{{110376&8/19}}}, 11th term = numerator = 8
{{{2^22 = 4194304}}}, 4194304÷19 = {{{220752&16/19}}}, 12th term = numerator = 16

This is the pattern, but I have no idea what it's called.  You continue it
for 10 more terms.

Edwin</pre>