perm filename SPEC23[MAX,DBL] blob
sn#197250 filedate 1976-01-17 generic text, type C, neo UTF8
COMMENT ⊗ VALID 00004 PAGES
C REC PAGE DESCRIPTION
C00001 00001
C00002 00002 3 simple examples, showing (for fixed D) how A2 and X depend on A1.
C00010 00003 The "best" real value for A2, and integral value for A1, given D. (to minimize X).
C00016 00004 The "ideal" A1 and A2 (both Real nos.) for a given D. (to minimize X).
C00020 ENDMK
C⊗;
3 simple examples, showing (for fixed D) how A2 and X depend on A1.
D=8, A1=0, so: A2=7.0, and X=2187.0 A2 is integral.
D=8, A1=1, so: A2=3.0, and X=54.0 A2 is integral.
D=8, A1=2, so: A2=1.7, and X=25.0
D=8, A1=3, so: A2=1.0, and X=24.0 A2 is integral.
D=8, A1=4, so: A2=.6, and X=30.9
D=8, A1=5, so: A2=.3, and X=46.2
D=8, A1=6, so: A2=.1, and X=74.9
D=8, A1=7, so: A2=0.0, and X=128.0 A2 is integral.
←
D=19, A1=0, so: A2=18.0, and X=3.874205E8 A2 is integral.
D=19, A1=1, so: A2=8.5, and X=22728.0
D=19, A1=2, so: A2=5.3, and X=1401.9
D=19, A1=3, so: A2=3.8, and X=492.4
D=19, A1=4, so: A2=2.8, and X=346.8
D=19, A1=5, so: A2=2.2, and X=345.9
D=19, A1=6, so: A2=1.7, and X=420.8
D=19, A1=7, so: A2=1.4, and X=579.8
D=19, A1=8, so: A2=1.1, and X=867.7
D=19, A1=9, so: A2=.9, and X=1376.2
D=19, A1=10, so: A2=.7, and X=2276.7
D=19, A1=11, so: A2=.6, and X=3887.3
D=19, A1=12, so: A2=.5, and X=6801.0
D=19, A1=13, so: A2=.4, and X=12128.0
D=19, A1=14, so: A2=.3, and X=21961.0
D=19, A1=15, so: A2=.2, and X=40263.4
D=19, A1=16, so: A2=.1, and X=74578.2
D=19, A1=17, so: A2=.1, and X=139321.0
D=19, A1=18, so: A2=0.0, and X=262144.0 A2 is integral.
←
D=36, A1=0, so: A2=35.0, and X=<TOO BIG> A2 is integral.
D=36, A1=1, so: A2=17.0, and X=2.582803E8 A2 is integral.
D=36, A1=2, so: A2=11.0, and X=708588.0 A2 is integral.
D=36, A1=3, so: A2=8.0, and X=52488.0 A2 is integral.
D=36, A1=4, so: A2=6.2, and X=14530.2
D=36, A1=5, so: A2=5.0, and X=7776.0 A2 is integral.
D=36, A1=6, so: A2=4.1, and X=6064.9
D=36, A1=7, so: A2=3.5, and X=5986.0
D=36, A1=8, so: A2=3.0, and X=6912.0 A2 is integral.
D=36, A1=9, so: A2=2.6, and X=8908.1
D=36, A1=10, so: A2=2.3, and X=12435.6
D=36, A1=11, so: A2=2.0, and X=18432.0 A2 is integral.
D=36, A1=12, so: A2=1.8, and X=28608.7
D=36, A1=13, so: A2=1.6, and X=46041.8
D=36, A1=14, so: A2=1.4, and X=76276.3
D=36, A1=15, so: A2=1.3, and X=129375.3
D=36, A1=16, so: A2=1.1, and X=223734.6
D=36, A1=17, so: A2=1.0, and X=393216.0 A2 is integral.
D=36, A1=18, so: A2=.9, and X=700548.0
D=36, A1=19, so: A2=.8, and X=1.262603E6
D=36, A1=20, so: A2=.7, and X=2.298269E6
D=36, A1=21, so: A2=.6, and X=4.219418E6
D=36, A1=22, so: A2=.6, and X=7.804357E6
D=36, A1=23, so: A2=.5, and X=1.45295E7
D=36, A1=24, so: A2=.4, and X=2.720528E7
D=36, A1=25, so: A2=.4, and X=5.11986E7
D=36, A1=26, so: A2=.3, and X=9.678773E7
D=36, A1=27, so: A2=.3, and X=1.837089E8
D=36, A1=28, so: A2=.2, and X=3.499509E8
D=36, A1=29, so: A2=.2, and X=6.687967E8
D=36, A1=30, so: A2=.2, and X=1.281902E9
D=36, A1=31, so: A2=.1, and X=2.463599E9
D=36, A1=32, so: A2=.1, and X=1.3101E9
D=36, A1=33, so: A2=.1, and X=2.291435E9
D=36, A1=34, so: A2=0.0, and X=5.478101E8
D=36, A1=35, so: A2=0.0, and X=0.0 A2 is integral.
The "best" real value for A2, and integral value for A1, given D. (to minimize X).
D=3, A1=1, so: A2=.5, and LOGX=1.2. A1+1= 2, and A2+1= 1.5
D=4, A1=2, so: A2=.3, and LOGX=1.8. A1+1= 3, and A2+1= 1.3
D=5, A1=2, so: A2=.7, and LOGX=2.1. A1+1= 3, and A2+1= 1.7
D=6, A1=2, so: A2=1.0, and LOGX=2.5. A1+1= 3, and A2+1= 2.0
D=7, A1=2, so: A2=1.3, and LOGX=2.9. A1+1= 3, and A2+1= 2.3
D=8, A1=3, so: A2=1.0, and LOGX=3.2. A1+1= 4, and A2+1= 2.0
D=9, A1=3, so: A2=1.3, and LOGX=3.5. A1+1= 4, and A2+1= 2.3
D=10, A1=3, so: A2=1.5, and LOGX=3.7. A1+1= 4, and A2+1= 2.5
D=11, A1=3, so: A2=1.8, and LOGX=4.0. A1+1= 4, and A2+1= 2.8
D=12, A1=3, so: A2=2.0, and LOGX=4.3. A1+1= 4, and A2+1= 3.0
D=13, A1=4, so: A2=1.6, and LOGX=4.5. A1+1= 5, and A2+1= 2.6
D=14, A1=4, so: A2=1.8, and LOGX=4.8. A1+1= 5, and A2+1= 2.8
D=15, A1=4, so: A2=2.0, and LOGX=5.0. A1+1= 5, and A2+1= 3.0
D=16, A1=4, so: A2=2.2, and LOGX=5.2. A1+1= 5, and A2+1= 3.2
D=17, A1=4, so: A2=2.4, and LOGX=5.4. A1+1= 5, and A2+1= 3.4
D=18, A1=4, so: A2=2.6, and LOGX=5.6. A1+1= 5, and A2+1= 3.6
D=19, A1=5, so: A2=2.2, and LOGX=5.8. A1+1= 6, and A2+1= 3.2
D=20, A1=5, so: A2=2.3, and LOGX=6.0. A1+1= 6, and A2+1= 3.3
←
D=30, A1=6, so: A2=3.3, and LOGX=7.8. A1+1= 7, and A2+1= 4.3
D=40, A1=7, so: A2=4.0, and LOGX=9.2. A1+1= 8, and A2+1= 5.0
D=50, A1=8, so: A2=4.6, and LOGX=10.5. A1+1= 9, and A2+1= 5.6
D=60, A1=9, so: A2=5.0, and LOGX=11.7. A1+1= 10, and A2+1= 6.0
D=70, A1=10, so: A2=5.4, and LOGX=12.8. A1+1= 11, and A2+1= 6.4
D=80, A1=10, so: A2=6.3, and LOGX=13.8. A1+1= 11, and A2+1= 7.3
D=90, A1=11, so: A2=6.5, and LOGX=14.8. A1+1= 12, and A2+1= 7.5
D=100, A1=12, so: A2=6.7, and LOGX=15.7. A1+1= 13, and A2+1= 7.7
D=110, A1=12, so: A2=7.5, and LOGX=16.5. A1+1= 13, and A2+1= 8.5
D=120, A1=13, so: A2=7.6, and LOGX=17.3. A1+1= 14, and A2+1= 8.6
D=130, A1=13, so: A2=8.3, and LOGX=18.1. A1+1= 14, and A2+1= 9.3
D=140, A1=14, so: A2=8.3, and LOGX=18.9. A1+1= 15, and A2+1= 9.3
D=150, A1=14, so: A2=9.0, and LOGX=19.6. A1+1= 15, and A2+1= 10.0
D=160, A1=15, so: A2=9.0, and LOGX=20.3. A1+1= 16, and A2+1= 10.0
D=170, A1=15, so: A2=9.6, and LOGX=21.0. A1+1= 16, and A2+1= 10.6
D=180, A1=16, so: A2=9.6, and LOGX=21.6. A1+1= 17, and A2+1= 10.6
D=190, A1=16, so: A2=10.2, and LOGX=22.3. A1+1= 17, and A2+1= 11.2
D=200, A1=17, so: A2=10.1, and LOGX=22.9. A1+1= 18, and A2+1= 11.1
←
D=1000, A1=39, so: A2=24.0, and LOGX=53.4. A1+1= 40, and A2+1= 25.0
D=6000, A1=97, so: A2=60.2, and LOGX=133.4. A1+1= 98, and A2+1= 61.2
D=11000, A1=131, so: A2=82.3, and LOGX=181.3. A1+1= 132, and A2+1= 83.3
D=36000, A1=238, so: A2=149.6, and LOGX=329.4. A1+1= 239, and A2+1= 150.6
D=96000, A1=389, so: A2=245.2, and LOGX=539.0. A1+1= 390, and A2+1= 246.2
←
D=5000000, A1=2814, so: A2=1775.2, and LOGX=3900.8. A1+1= 2815, and A2+1= 1776.2
D=50000000, A1=8901, so: A2=5615.7, and LOGX=12339.2. A1+1= 8902, and A2+1= 5616.7
D=1000000000, A1=39800, so: A2=25124.0, and LOGX=55188.8. A1+1= 39,801, and A2+1= 25,125.0
********************************************************************************
LOG(2) = .6931472
LOG(3) = 1.098612
1 / LOG(2) = 1.442695
1 / LOG(3) = .9102392
1 / (LOG(2) x LOG(3)) = 1.313198
←
Consider the case when D=1,313,198 or D=13,132:
D=13132, A1=143, so: A2=90.2, and LOGX=198.2. A1+1= 144, and A2+1= 91.2
D=1313198, A1=1442, so: A2=909.0, and LOGX=1998.2. A1+1= 1443, and A2+1= 910.0
The "ideal" A1 and A2 (both Real nos.) for a given D. (to minimize X).
D=2, Optimal A1=.8, A2=.1, and LOGX=.7
D=3, Optimal A1=1.2, A2=.4, and LOGX=1.2
D=4, Optimal A1=1.5, A2=.6, and LOGX=1.7
D=5, Optimal A1=1.8, A2=.8, and LOGX=2.1
D=6, Optimal A1=2.1, A2=.9, and LOGX=2.5
D=7, Optimal A1=2.3, A2=1.1, and LOGX=2.8
D=8, Optimal A1=2.6, A2=1.2, and LOGX=3.1
D=9, Optimal A1=2.8, A2=1.4, and LOGX=3.4
D=10, Optimal A1=3.0, A2=1.5, and LOGX=3.7
D=11, Optimal A1=3.2, A2=1.6, and LOGX=4.0
D=12, Optimal A1=3.4, A2=1.8, and LOGX=4.3
D=13, Optimal A1=3.5, A2=1.9, and LOGX=4.5
D=14, Optimal A1=3.7, A2=2.0, and LOGX=4.7
D=15, Optimal A1=3.9, A2=2.1, and LOGX=5.0
D=16, Optimal A1=4.0, A2=2.2, and LOGX=5.2
D=17, Optimal A1=4.2, A2=2.3, and LOGX=5.4
D=18, Optimal A1=4.3, A2=2.4, and LOGX=5.6
D=19, Optimal A1=4.5, A2=2.5, and LOGX=5.8
D=20, Optimal A1=4.6, A2=2.6, and LOGX=6.0
←
D=30, Optimal A1=5.9, A2=3.4, and LOGX=7.8
D=40, Optimal A1=7.0, A2=4.0, and LOGX=9.2
D=50, Optimal A1=7.9, A2=4.6, and LOGX=10.5
D=60, Optimal A1=8.8, A2=5.2, and LOGX=11.7
D=70, Optimal A1=9.5, A2=5.6, and LOGX=12.8
D=80, Optimal A1=10.3, A2=6.1, and LOGX=13.8
D=90, Optimal A1=10.9, A2=6.5, and LOGX=14.8
D=100, Optimal A1=11.6, A2=6.9, and LOGX=15.7
D=110, Optimal A1=12.2, A2=7.3, and LOGX=16.5
D=120, Optimal A1=12.8, A2=7.7, and LOGX=17.3
D=130, Optimal A1=13.4, A2=8.1, and LOGX=18.1
D=140, Optimal A1=13.9, A2=8.4, and LOGX=18.9
D=150, Optimal A1=14.4, A2=8.7, and LOGX=19.6
D=160, Optimal A1=14.9, A2=9.0, and LOGX=20.3
D=170, Optimal A1=15.4, A2=9.4, and LOGX=21.0
D=180, Optimal A1=15.9, A2=9.7, and LOGX=21.6
D=190, Optimal A1=16.4, A2=9.9, and LOGX=22.3
D=200, Optimal A1=16.8, A2=10.2, and LOGX=22.9
←
D=1000, Optimal A1=38.8, A2=24.1, and LOGX=53.4
D=96000, Optimal A1=389.1, A2=245.1, and LOGX=539.0
D=5000000, Optimal A1=2814.1, A2=1775.1, and LOGX=3900.8
D=50000000, Optimal A1=8901.1, A2=5615.6, and LOGX=12339.2
D=1000000000, Optimal A1=39810.6, A2=25117.3, and LOGX=55188.8
←
D=13132, Optimal A1=143.3, A2=90.0, and LOGX=198.2
D=1313198, Optimal A1=1441.7, A2=909.2, and LOGX=1998.2