1 = 2^2/3^1=4/3
  2 = 2^3/3^1=8/3
  3 = 2^5/3^2=32/9
  4 = 2^7/3^3=128/27
  5 = 2^4/3^1=16/3
  6 = 2^9/3^4=512/81
  7 = 2^6/3^2=64/9
  8 = 2^11/3^5=2048/243
  9 = 2^8/3^3=256/27
 10 = 2^5/3^1=32/3
 11 = 2^13/3^6=8192/729
 12 = 2^10/3^4=1024/81
 13 = 2^18/3^9=262144/19683
 14 = 2^7/3^2=128/9
 15 = 2^23/3^12=8388608/531441
 16 = 2^12/3^5=4096/243
 17 = 2^20/3^10=1048576/59049
 18 = 2^9/3^3=512/27
 19 = 2^17/3^8=131072/6561
 20 = 2^44/3^25=17592186044416/847288609443
 21 = 2^6/3^1=64/3
 22 = 2^14/3^6=16384/729
 23 = 2^22/3^11=4194304/177147
 24 = 2^30/3^16=1073741824/43046721
 25 = 2^11/3^4=2048/81
 26 = 2^19/3^9=524288/19683
 27 = 2^46/3^26=70368744177664/2541865828329
 28 = 2^8/3^2=256/9
 29 = 2^16/3^7=65536/2187
 30 = 2^62/3^36=4611686018427387904/150094635296999121
 31 = 2^24/3^12=16777216/531441
 32 = 2^51/3^29=2251799813685248/68630377364883
 33 = 2^13/3^5=8192/243
 34 = 2^59/3^34=576460752303423488/16677181699666569
 35 = 2^21/3^10=2097152/59049
 36 = 2^48/3^27=281474976710656/7625597484987
 37 = 2^10/3^3=1024/27
 38 = 2^56/3^32=72057594037927936/1853020188851841
 39 = 2^18/3^8=262144/6561