q3=11
【∑[k=1,3.q≠q+2]qk】=19
4*11^2=484
1/3=0.3333333333
484^1.3333333333=3800
3800/19=200
ln3800^2=67.9430321746
67.9430321746/200=0.3397151609
c[+]3=0.3397151609

1-0.3333333333=0.6666666667
484^0.6666666667=61.6448652871
61.6448652871/19=3.2444665941
ln61.6448652871^2=16.9858550210
16.9858550210/3.2444665941=5.2353305323
c[-]3=5.2353305323

c[+]3=0.3397151609
0.3397151609*10^3=339.7151609000
ln1000^2=47.7170829946
339.7151609000/47.7170829946=7.1193614442
4/3=1.3333333333
7.1193614442*1.3333333333=9.4924819254
D(10^3)=28

c[-]3=5.2353305323
5.2353305323*10^3=5235.3305323
5235.3305323/47.7170829946=109.7160640120
109.7160640120*1.3333333333=146.2880853457

q6=41
4*41^2=6724
1/6=0.1666666667
6724^1.1666666667=29212.2935188902
29212.2935188902/106=275.5876747065
ln29212.2935188902^2=105.7266168605
105.7266168605/275.5876747065=0.3836405854
c[+]6=0.3836405854

1-0.1666666667=0.8333333333
6724^0.8333333333=1547.7105887206
1547.7105887206/106=14.6010432898
ln1547.7105887206^2=53.9421514521
53.9421514521/14.6010432898=3.6944039122
c[-]6=3.6944039122

c[+]6=0.3836405854
0.3836405854*10000=3836.405854
ln10000^2=84.8303697681
3836.405854/84.8303697681=45.2244386590
4/3=1.3333333333
45.2244386590*1.3333333333=60.2992515438
D(10^4)=127

c[-]6=3.6944039122
3.6944039122*10^4=36944.039122
36944.039122/84.8303697681=435.5048695767
435.5048695767*1.3333333333=580.6731594211

@铁枪快马 2016-07-07 10:45:23
虽然看不懂，但支持一下。
-----------------------------
谢谢朋友！

q12=149
【∑[k=1,12.q≠q+2]qk】=730
4*149^2=88804
1/12=0.0833333333
88804^1.0833333333=229510.1545055011
229510.1545055011/730=314.3974719253
ln229510.1545055011^2=152.3669927342
152.3669927342/314.3974719253=0.4846317364
c[+]12=0.4846317364

1-0.0833333333=0.9166666667
88804^0.9166666667=34360.7908460145
34360.7908460145/730=47.0695765014
ln34360.7908460145^2=109.0911604931
109.0911604931/47.0695765014=2.3176575742
c[-]12=2.3176575742

c[+]12=0.4846317364
0.4846317364*10^5=48463.17364
ln100000^2=132.5474527626
48463.17364/132.5474527626=365.6288569106
4/3=1.3333333333
365.6288569106*1.3333333333=487.5051425353
D(10^5)=810

c[-]12=2.3176575742
2.3176575742*10^5=231765.75742
231765.75742/132.5474527626=1748.5493126383

q24=461
【∑[k=1,24.q≠q+2]qk】=4282
4*461^2=850084
1/24=0.0416666667
850084^1.0416666667=1501491.0657899978
1501491.0657899978/4282=350.6518135894
ln1501491.0657899978^2=202.2644083865
202.2644083865/350.6517982251=0.5768241013
c[+]24=0.5768241013

1-0.0416666667=0.9583333333
850084^0.9583333333=481283.4545077950
481283.4545077950/4282=112.3968833507
ln481283.4545077950^2=171.1965952347
171.1965952347/112.3968833507=1.5231436151
c[-]24=1.5231436151

c[+]24=0.5768241013
0.5768241013*10^6=576824.1013
ln1000000^2=190.8683319782
576824.1013/190.8683319782=3022.1047950787
4/3=1.3333333333
3022.1047950787*1.3333333333=4029.4730600042
D(10^6)>4029.4730600042
D(10^6)=5402

c[-]24=1.5231436151
1.5231436151*10^6=1523143.6151
1523143.6151/190.8683319782=7980.0750565262
7980.0750565262*1.3333333333=10640.1000751023

q50=1487
【∑[k=1,50.q≠q+2]qk】=30746
4*1487^2=8844676
1/50=0.02
8844676^1.02=12179110.391586652
12179110.391586652/30746=396.12015844619305
ln12179110.391586652^2=266.1868206369045
266.1868206369045/396.12015844619305=0.671985040299488
c[+]50=0.671985040299488

1-0.02=0.98
8844676^0.98=6423153.336307406
6423153.336307406/30746=208.91021063902318
ln6423153.336307406^2=245.71878367904947
245.71878367904947/208.91021063902318=1.176193269478953
c[-]50=1.176193269478953

c[+]50=0.671985040299488
0.671985040299488*10^7=6719850.40299488
ln10000000^2=259.7930074148
6719850.40299488/259.7930074148=25866.17118706968
4/3=1.3333333333
25866.17118706968*1.3333333333=34488.22824856403
D(10^7)>34488.22824856403
D(10^7)=38807

c[-]50=1.176193269478953
1.176193269478953*10^7=11761932.69478953
11761932.69478953/259.7930074148=45274.246646715066
45274.246646715066*1.3333333333=60365.66219411094

从q51开始，我们使用f(x)=1/lnx




q126=4967
【∑[k=1,126.q≠q+2]qk】=277144
4*4967^2=98684356
ln98684356=18.407436991334592
1/18.407436991334592=0.054325868423222
98684356^1.054325868423222=268251891.66798112
268251891.66798112/277144=967.9152053372294
ln268251891.66798112^2=376.648610572622
376.648610572622/967.9152053372294=0.389133891580301
c[+]126=0.389133891580301

1-0.054325868423222=0.945674131576778
98684356^0.945674131576778=36303945.73764397
36303945.73764397/277144=130.99307846334025
ln36303945.73764397^2=303.0188626072842
303.0188626072842/130.99307846334025=2.313243311493646
c[-]126=2.313243311493646

c[+]126=0.389133891580301
0.389133891580301*10^8=38913389.1580301
ln100000000^2=339.32147907061756
38913389.1580301/339.32147907061756=114680.00571202178
4/3=1.3333333333
114680.00571202178*1.3333333333=152906.67427887305
D(10^8)=291400

c[-]126=2.313243311493646
2.313243311493646*10^8=231324331.1493646
231324331.1493646/339.32147907061756=681726.1665337217
681726.1665337217*1.3333333333=908968.2220222381

q282=15737
【∑[k=1,282.q≠q+2]qk】=1844038
4*15737^2=990612676
ln990612676=20.71383417432162
1/20.71383417432162=0.048276914432369
990612676^1.048276914432369=2692764436.2119985
2692764436.2119985/1844038=1460.2543094079397
ln2692764436.2119985^2=471.49059454993755
471.49059454993755/1460.2543094079397=0.322882522251281
c[+]282=0.322882522251281

1-0.048276914432369=0.951723085567631
990612676^0.951723085567631=364426037.66422474
364426037.66422474/1844038=197.62393056120575
ln364426037.66422474^2=388.6352578526507
388.6352578526507/197.62393056120575=1.966539460828541
c[-]282=1.966539460828541

c[+]282=0.322882522251281
0.322882522251281*10^9=322882522.251281
ln1000000000^2=429.453746948733
322882522.251281/429.453746948733=751844.6970025526
6197878.980125919
751844.6970025526*1.3333333333=1002459.5959783418
D(10^9)=2274205

c[-]282=1.966539460828541
1.966539460828541*10^9=1966539460.828541
1966539460.828541/429.453746948733=4579164.7524344480
4579164.7524344480*1.3333333333=6105553.0030932920

q705=49991
【∑[k=1,705.q≠q+2]qk】=15469207
4*49991^2=9996400324
ln9996400324=23.025490897536567
1/23.025490897536567=0.04343012726417
9996400324^1.04343012726417=27173033350.731308
27173033350.731308/15469207=1756.5886441839784
ln27173033350.731308^2=577.2242128676124
577.2242128676124/1756.5886441839784=0.328605228537021
c[+]705=0.328605228537021

1-0.04343012726417=0.95656987273583
9996400324^0.95656987273583=3677470164.919145
3677470164.919145/15469207=237.72842169085624
ln3677470164.919145^2=485.12224927746615
485.12224927746615/237.72842169085624=2.040657342639168
c[-]705=2.040657342639168

c[+]705=0.328605228537021
0.328605228537021*10^10=3286052285.37021
ln10^10^2=530.189811047819
3286052285.37021/530.189811047819=6197878.980125919
6197878.980125919*1.3333333333=8263838.639961295
D(10^10)=18200488

c[-]705=2.040657342639168
2.040657342639168*10^10=20406573426.39168
20406573426.39168/530.189811047819=38489184.44143991
38489184.44143991*1.3333333333=51318912.58730357

q1785=157931
【∑[k=1,1785.q≠q+2]qk】=126995779
4*157931^2=99768803044
ln99768803044=25.32612137664641
1/25.32612137664641=0.039484924877684
99768803044^1.039484924877684=271199724361.61252
271199724361.61252/126995779=2135.5018764963243
ln271199724361.61252^2=693.0646667379186
693.0646667379186/2135.5018764963243=0.324544161897444
c[+]1785=0.324544161897444

1-0.039484924877684=0.960515075122316
99768803044^0.960515075122316=36702891510.17081
36702891510.17081/126995779=289.0087513079534
ln36702891510.17081^2=591.7601812313338
591.7601812313338/289.0087513079534=2.047551081250075
c[-]1785=2.047551081250075

c[+]1785=0.324544161897444
0.324544161897444*10^11=32454416189.7444
ln10^11^2=641.529671367911
32454416189.7444/641.529671367911=50589111.67825333
50589111.67825333*1.3333333333=67452148.90265146
D(10^11)=149091160

c[-]1785=2.047551081250075
2.047551081250075*10^11=204755108125.0075
204755108125.0075/641.529671367911=319167011.69630307
319167011.69630307*1.3333333333=425556015.5844318

q4565=499691
4*499691^2=998764381924
1/4565=0.000219058050383
998764381924^1.000219058050383=1004827760960.7836
1004827760962/1025782751=979.5717075398551
ln1004827760962^2=763.7395010957284
763.7395010957284/979.5717075398551=0.779666761725716
c4565=0.779666761725716

c4565=0.779666761725716
0.779666761725716*10^12=779666761725.716
ln10^12^2=763.473327908914
779666761725.716/763.473327908914=1021210215.50439
4/3=1.3333333333
1021210215.50439*1.3333333333=1361613620.6384795
D(10^12)
D(10^12)=1243722370

q4565=499691
【∑[k=1,4565.q≠q+2]qk】=1025782751
4*499691^2=998764381924
ln998764381924=27.629784733847124
1/27.629784733847124=0.036192826315255
998764381924^1.036192826315255=2714923070296.166
2714923070296.166/1025782751=2646.684268817625
ln2714923070296.166^2=819.6645739064263
819.6645739064263/2646.684268817625=0.30969488259837
c[+]4565=0.30969488259837

1-0.036192826315255=0.963807173684745
998764381924^0.963807173684745=367424882684.1373
367424882684.1373/1025782751=358.18976515831207
ln367424882684.1373^2=709.1454349710368
709.1454349710368/358.18976515831207=1.979803735200558
c[-]4565=1.979803735200558

c[+]4565=0.30969488259837
0.30969488259837*10^12=309694882598.37
ln10^12^2=763.473327908914
309694882598.37/763.473327908914=405639426.12978625
405639426.12978625*1.3333333333=540852568.159527
D(10^12)=1243722370

c[-]4565=1.979803735200558
1.979803735200558*10^12=1979803735200.558
1979803735200.558/763.473327908914=2593153765.5978966
2593153765.5978966*1.3333333333=3457538354.0440903

c[0]k的计算：
x

c[0]k的计算：
x→∞双记法c[0]k→1
x→∞简记法c[0]k→0.5




q1=3
【∑[k=1,1.q≠q+2]qk】=3
4*3^2=36
ln36^2=12.8416079826
36/3=12
12/12.8416079826=0.9344624144
1/0.9344624144=1.0701339985
c[0]1=1.0701339985

@施承忠 2016-07-10 14:46:12
c[0]k的计算：
x→∞双记法c[0]k→1
x→∞简记法c[0]k→0.5
q1=3
【∑[k=1,1.q≠q+2]qk】=3
4*3^2=36
ln36^2=12.8416079826
36/3=12
12/12.8416079826=0.9344624144
1/0.9344624144=1.0701339985
c[0]1=1.0701339985
-----------------------------
x→∞单记法c[0]k→0.5

c[0]k是一个可以计算D(x)的近似值的系数。
因为c[0]1是最初的一个系数。
4*q1^2=36
4*q2^2=100
所以c[0]1适用于6至98
c[0]1=1.0701339985

1.0701339985*6=6.4208039910
(ln6)^2=3.2104019955
6.4208039910/3.2104019955=2
2*3-1/3-2=4
D(6)≈4
D(6)=1

1.0701339985*8=8.5610719880
(ln8)^2=4.3240771253
8.5610719880/4.3240771253=1.9798610755
D(8)≈1.9798610755
D(8)=1

1.0701339985*10=10.701339985
(ln10)^2=5.3018981105
10.701339985/5.3018981105=2.0183978949
2.0183978949*5-1/5-2=2.6911971931
D(10)≈2.6911971931
D(10)=2

1.0701339985*12=12.8416079820
(ln12)^2=6.1747610582
12.8416079820/6.1747610582=2.0796931024
2.0796931024*3-1/3-2=4.1593862048
D(12)≈4.1593862048
D(12)=1