Processing math: 100%
 

heureka

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 #1
avatar+26397 
+15

Please give the next 4 terms of this sequence. Thanks for any help:

2, 4, 7, 10, 15, 18, 23, 26............640 (is 100th term)

 

We need the prime number table

 

The prime numbers. np(n)np(n)np(n)np(n)np(n)np(n)1221734117961283814191015472322794218162293824213523834319163307834314724894419364311844335112597451976531385439613261014619966317864437172710347211673318744981928107482236833788457923291094922769347894611029301135022970349904631131311275123371353914671237321315223972359924791341331375324173367934871443341395425174373944911547351495525775379954991653361515626376383965031759371575726977389975091861381635827178397985211967391675927779401995232071401736028180409100541

 

The formula is  an=an1+p(n)p(n1)+1n2a1=2 

 

a1=2a2=a1+p(2)p(1)+1=2+32+1=4a3=a2+p(3)p(2)+1=4+53+1=7a4=a3+p(4)p(3)+1=7+75+1=10a5=a4+p(5)p(4)+1=10+117+1=15a6=a5+p(6)p(5)+1=15+1311+1=18a7=a6+p(7)p(6)+1=18+1713+1=23a8=a7+p(8)p(7)+1=23+1917+1=26a9=a8+p(9)p(8)+1=26+2319+1=31a10=a9+p(10)p(9)+1=31+2923+1=38a11=a10+p(11)p(10)+1=38+3129+1=41a12=a11+p(12)p(11)+1=41+3731+1=48a100=a99+p(100)p(99)+1=621+541523+1=640

 

a1a50na(n)na(n)na(n)na(n)na(n)1211412193311574121924124822100321624222237135323105331694323341014562411234172442365151561251213518345241618166826126361864624472317752712937193472578261878281343820048270931198529137392054927510382090301424021250278

 

a51a101na(n)na(n)na(n)na(n)na(n)na(n)51283613437142381499915571016475229062354724308250292570532936336973439835139357954304643747444684516945845531165377754538552395593563186638276458865289659857325673977746587535976055832868404784748854498618593356941579479895499962160340704188048890552100640

 

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14.01.2016
 #1
avatar+26397 
+25

Using US coins of 1¢, 5¢, 10¢, 25¢, 50¢, and $1, how many ways are there to make change for $1.00.  List all the ways.

 

Number1 Cent5 Cent10 Cent25 Cent50 Cent$11.100=12.100=23.100=214.100=45.100=516.100=527.100=108.100=12119.100=12310.100=17111.100=24112.100=24213.100=2914.100=311115.100=31316.100=36117.100=43118.100=43219.100=4820.100=51121.100=5322.100=55123.100=62124.100=62225.100=6726.100=74127.100=81128.100=81229.100=8630.100=93131.100=10132.100=10233.100=10534.100=112135.100=12436.100=131137.100=14338.100=15139.100=16240.100=18141.100=2042.100=521143.100=52344.100=57145.100=514146.100=514247.100=51948.100=5211149.100=521350.100=526151.100=533152.100=533253.100=53854.100=541155.100=54356.100=545157.100=552158.100=552259.100=55760.100=564161.100=571162.100=571263.100=57664.100=583165.100=59166.100=59267.100=59568.100=5102169.100=511470.100=5121171.100=513372.100=514173.100=515274.100=517175.100=51976.100=104177.100=104278.100=10979.100=10111180.100=1011381.100=1016182.100=1023183.100=1023284.100=102885.100=1031186.100=103387.100=1035188.100=1042189.100=1042290.100=104791.100=1054192.100=1061193.100=1061294.100=106695.100=1073196.100=108197.100=108298.100=108599.100=10921100.100=10104101.100=101111102.100=10123103.100=10131104.100=10142105.100=10161106.100=1018107.100=15111108.100=1513109.100=1561110.100=15131111.100=15132112.100=1518113.100=15211114.100=1523115.100=15251116.100=15321117.100=15322118.100=1537119.100=15441120.100=15511121.100=15512122.100=1556123.100=15631124.100=1571125.100=1572126.100=1575127.100=15821128.100=1594129.100=151011130.100=15113131.100=15121132.100=15132133.100=15151134.100=1517135.100=2031136.100=2032137.100=208138.100=20111139.100=2013140.100=20151141.100=20221142.100=20222143.100=2027144.100=20341145.100=20411146.100=20412147.100=2046148.100=20531149.100=2061150.100=2062151.100=2065152.100=20721153.100=2084154.100=20911155.100=20103156.100=20111157.100=20122158.100=20141159.100=2016160.100=2511161.100=253162.100=2551163.100=25121164.100=25122165.100=2517166.100=25241167.100=25311168.100=25312169.100=2536170.100=25431171.100=2551172.100=2552173.100=2555174.100=25621175.100=2574176.100=25811177.100=2593178.100=25101179.100=25112180.100=25131181.100=2515182.100=3021183.100=3022184.100=307185.100=30141186.100=30211187.100=30212188.100=3026189.100=30331190.100=3041191.100=3042192.100=3045193.100=30521194.100=3064195.100=30711196.100=3083197.100=3091198.100=30102199.100=30121200.100=3014201.100=3541202.100=35111203.100=35112204.100=3516205.100=35231206.100=3531207.100=3532208.100=3535209.100=35421210.100=3554211.100=35611212.100=3573213.100=3581214.100=3592215.100=35111216.100=3513217.100=4011218.100=4012219.100=406220.100=40131221.100=4021222.100=4022223.100=4025224.100=40321225.100=4044226.100=40511227.100=4063228.100=4071229.100=4082230.100=40101231.100=4012232.100=4531233.100=4511234.100=4512235.100=4515236.100=45221237.100=4534238.100=45411239.100=4553240.100=4561241.100=4572242.100=4591243.100=4511244.100=501245.100=502246.100=505247.100=50121248.100=5024249.100=50311250.100=5043251.100=5051252.100=5062253.100=5081254.100=5010255.100=5521256.100=5514257.100=55211258.100=5533259.100=5541260.100=5552261.100=5571262.100=559263.100=604264.100=60111265.100=6023266.100=6031267.100=6042268.100=6061269.100=608270.100=6511271.100=6513272.100=6521273.100=6532274.100=6551275.100=657276.100=703277.100=7011278.100=7022279.100=7041280.100=706281.100=751282.100=7512283.100=7531284.100=755285.100=802286.100=8021287.100=804288.100=8511289.100=853290.100=901291.100=902292.100=951293.100=100

 

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13.01.2016
 #1
avatar+26397 
+15

What is this equal to? 1+4+9+16+25...

Don't say that it is infinity.

 

 

d0=12223242521. Difference d1=3579112. Difference d2=22222

 

 

sn=(n1)d0+(n2)d1+(n3)d2sn=(n1)1+(n2)3+(n3)2(n1)=n(n2)=(n2)(n11)(n3)=(n3)(n12)(n21)sn=(n)1+(n2)(n11)3+(n3)(n12)(n21)2|66sn=n6+n(n1)9+n(n1)(n2)26sn=n[ 6+(n1)9+(n1)(n2)2 ]6sn=(n)[ 6+9n9+(n23n+2)2 ]6sn=(n)[ 3+9n+(n23n+2)2 ]6sn=(n)( 3+9n+2n26n+4 )6sn=(n)( 1+3n+2n2 )6sn=(n)(n+1)(2n+1)sn=(n)(n+1)(2n+1)6s1=1=1(1+1)(21+1)6=1s2=1+4=2(2+1)(22+1)6=5s3=1+4+9=3(3+1)(23+1)6=14s4=1+4+9+16=4(4+1)(24+1)6=30s5=1+4+9+16+25=5(5+1)(25+1)6=55

 

laugh

13.01.2016