Composite numbers k with no single digit factors whose factors are all substrings of k: Difference between revisions
(→{{header|Perl}}: prepend pascal version reused http://rosettacode.org/wiki/Factors_of_an_integer#using_Prime_decomposition) |
m (→{{header|Free Pascal}}: tested til 1E10) |
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Line 195: | Line 195: | ||
chk,p,i: NativeInt; |
chk,p,i: NativeInt; |
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Begin |
Begin |
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str(n,s); |
str(n:12,s); |
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result := s+': '; |
result := s+': '; |
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with pd^ do |
with pd^ do |
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Line 409: | Line 409: | ||
T0:Int64; |
T0:Int64; |
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n,i : NativeUInt; |
n,i,cnt : NativeUInt; |
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checked : boolean; |
checked : boolean; |
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Begin |
Begin |
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Line 415: | Line 415: | ||
T0 := GetTickCount64; |
T0 := GetTickCount64; |
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cnt := 0; |
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n := 0; |
n := 0; |
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Init_Sieve( |
Init_Sieve(n); |
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repeat |
repeat |
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pPrimeDecomp:= GetNextPrimeDecomp; |
pPrimeDecomp:= GetNextPrimeDecomp; |
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Line 422: | Line 423: | ||
begin |
begin |
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//composite with smallest factor 11 |
//composite with smallest factor 11 |
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if (pfDivCnt> |
if (pfDivCnt>=4) AND (pfpotPrimIdx[0]>3) then |
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begin |
begin |
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str(n,s); |
str(n,s); |
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Line 434: | Line 435: | ||
if checked then |
if checked then |
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begin |
begin |
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//writeln(cnt:4,OutPots(pPrimeDecomp,n)); |
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if pfRemain >1 then |
if pfRemain >1 then |
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begin |
begin |
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Line 440: | Line 442: | ||
end; |
end; |
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if checked then |
if checked then |
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begin |
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inc(cnt); |
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writeln(cnt:4,OutPots(pPrimeDecomp,n)); |
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end; |
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end; |
end; |
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end; |
end; |
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end; |
end; |
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inc(n); |
inc(n); |
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until n > 28118827;//1000*1000*1000+1;// |
until n > 28118827;//10*1000*1000*1000+1;// |
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T0 := GetTickCount64-T0; |
T0 := GetTickCount64-T0; |
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writeln('runtime ',T0/1000:0:3,' s'); |
writeln('runtime ',T0/1000:0:3,' s'); |
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Line 451: | Line 456: | ||
</lang> |
</lang> |
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{{out|@TIO.RUN}} |
{{out|@TIO.RUN}} |
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<pre style="height:480px"> |
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<pre> |
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Real time: 2.166 s CPU share: 99.20 %//500*1000*1000 Real time: 38.895 s CPU share: 99.28 % |
Real time: 2.166 s CPU share: 99.20 %//500*1000*1000 Real time: 38.895 s CPU share: 99.28 % |
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1 15317: 17^2*53 |
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2 59177: 17*59^2 |
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3 83731: 31*37*73 |
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4 119911: 11^2*991 |
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5 183347: 47^2*83 |
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6 192413: 13*19^2*41 |
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7 1819231: 19*23^2*181 |
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8 2111317: 13^3*31^2 |
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1819231 : 12 : 19*23^2*181 |
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9 2237411: 11^3*41^2 |
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10 3129361: 29^2*61^2 |
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11 5526173: 17*61*73^2 |
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12 11610313: 11^4*13*61 |
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13 13436683: 13^2*43^3 |
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11610313 : 20 : 11^4*13*61 |
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14 13731373: 73*137*1373 |
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13436683 : 12 : 13^2*43^3 |
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15 13737841: 13^5*37 |
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13731373 : 8 : 73*137*1373 |
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16 13831103: 11*13*311^2 |
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13737841 : 12 : 13^5*37 |
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17 15813251: 251^3 |
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13831103 : 12 : 11*13*311^2 |
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18 17692313: 23*769231 |
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15813251 : 4 : 251^3 |
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19 19173071: 19^2*173*307 |
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17692313 : 4 : 23*769231 |
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20 28118827: 11^2*281*827 |
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28118827 : 12 : 11^2*281*827 |
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runtime 2.011 s |
runtime 2.011 s |
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..@home limit 1E9 53^2*89xprime appears often |
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//@home til 1E10 .. 188 9898707359: 59^2*89^2*359 |
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21 31373137: 73*137*3137 |
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889253557 889253557 : 12 : 53^2*89*3557 |
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22 47458321: 83^4 |
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889753559 889753559 : 12 : 53^2*89*3559 |
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23 55251877: 251^2*877 |
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24 62499251: 251*499^2 |
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892961737 892961737 : 24 : 17^2*37^3*61 |
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25 79710361: 103*797*971 |
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895253581 895253581 : 12 : 53^2*89*3581 |
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26 81227897: 89*97^3 |
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27 97337269: 37^2*97*733 |
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28 103192211: 19^2*31*9221 |
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29 107132311: 11^2*13^4*31 |
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30 119503483: 11*19*83^3 |
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runtime 45.922 s |
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31 119759299: 11*19*29*19759 |
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32 124251499: 499^3 |
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33 131079601: 107^4 |
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34 142153597: 59^2*97*421 |
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35 147008443: 43^5 |
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36 171197531: 17^2*31*97*197 |
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37 179717969: 71*79*179^2 |
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38 183171409: 71*1409*1831 |
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39 215797193: 19*1579*7193 |
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40 241153517: 11*17*241*5351 |
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41 248791373: 73*373*9137 |
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42 261113281: 11^2*13^2*113^2 |
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43 272433191: 19*331*43319 |
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44 277337147: 71*73^2*733 |
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45 291579719: 19*1579*9719 |
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46 312239471: 31^3*47*223 |
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47 344972429: 29*3449^2 |
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48 364181311: 13^4*41*311 |
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49 381317911: 13^6*79 |
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50 385494799: 47^4*79 |
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51 392616923: 23^5*61 |
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52 399311341: 11*13^4*31*41 |
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53 410963311: 11^2*31*331^2 |
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54 413363353: 13^4*41*353 |
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55 423564751: 751^3 |
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56 471751831: 31*47^2*83^2 |
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57 492913739: 73*739*9137 |
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58 501225163: 163*251*12251 |
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59 591331169: 11*13^2*31^2*331 |
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60 592878929: 29^2*89^3 |
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61 594391193: 11*19^2*43*59^2 |
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62 647959343: 47^3*79^2 |
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63 717528911: 11^2*17^4*71 |
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64 723104383: 23^2*43*83*383 |
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65 772253089: 53^2*89*3089 |
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66 799216219: 79^3*1621 |
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67 847253389: 53^2*89*3389 |
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68 889253557: 53^2*89*3557 |
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69 889753559: 53^2*89*3559 |
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70 892753571: 53^2*89*3571 |
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71 892961737: 17^2*37^3*61 |
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72 895253581: 53^2*89*3581 |
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73 895753583: 53^2*89*3583 |
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74 898253593: 53^2*89*3593 |
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75 972253889: 53^2*89*3889 |
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76 997253989: 53^2*89*3989 |
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77 1005371999: 53^2*71^3 |
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78 1011819919: 11*101*919*991 |
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79 1019457337: 37^2*73*101^2 |
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80 1029761609: 29^2*761*1609 |
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81 1031176157: 11^2*17*31*103*157 |
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82 1109183317: 11*31^2*317*331 |
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83 1119587711: 11^2*19^4*71 |
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84 1137041971: 13^4*41*971 |
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85 1158169331: 11*31^2*331^2 |
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86 1161675547: 47^3*67*167 |
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87 1189683737: 11^5*83*89 |
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88 1190911909: 11*9091*11909 |
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89 1193961571: 11^3*571*1571 |
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90 1274418211: 11*41^5 |
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91 1311979279: 13^2*19*131*3119 |
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92 1316779217: 13^2*17*677^2 |
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93 1334717327: 47*73^4 |
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94 1356431947: 13*43^2*56431 |
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95 1363214333: 13^3*433*1433 |
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96 1371981127: 11^2*19*37*127^2 |
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97 1379703847: 47^3*97*137 |
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98 1382331137: 11*31*37*331^2 |
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99 1389214193: 41*193*419^2 |
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100 1497392977: 97*3929^2 |
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101 1502797333: 733^2*2797 |
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102 1583717977: 17^2*71*79*977 |
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103 1593519731: 59*5197^2 |
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104 1713767399: 17^6*71 |
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105 1729719587: 17*19^2*29*9719 |
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106 1733793487: 79^2*379*733 |
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107 1761789373: 17^2*37^2*61*73 |
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108 1871688013: 13^5*71^2 |
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109 1907307719: 71^3*73^2 |
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110 1948441249: 1249^3 |
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111 1963137527: 13*31^3*37*137 |
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112 1969555417: 17*41^5 |
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113 1982119441: 211^4 |
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114 1997841197: 11*97^3*199 |
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115 2043853681: 53^2*853^2 |
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116 2070507919: 19^2*79^2*919 |
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117 2073071593: 73^5 |
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118 2278326179: 17*83*617*2617 |
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119 2297126743: 29^3*97*971 |
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120 2301131209: 13^4*23*31*113 |
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121 2323519823: 19^2*23^5 |
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122 2371392959: 13^2*29*59^2*139 |
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123 2647985311: 31*47*53^2*647 |
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124 2667165611: 11^5*16561 |
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125 2722413361: 241*3361^2 |
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126 2736047519: 19^2*47^3*73 |
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127 2881415311: 31^3*311^2 |
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128 2911317539: 13^2*31*317*1753 |
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129 2924190611: 19^3*29*61*241 |
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130 3015962419: 41*419^3 |
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131 3112317013: 13^2*23^2*31*1123 |
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132 3131733761: 13^2*17^2*37*1733 |
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133 3150989441: 41*509*150989 |
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134 3151811881: 31^2*1811^2 |
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135 3423536177: 17*23^2*617^2 |
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136 3461792569: 17^2*3461^2 |
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137 3559281161: 281*3559^2 |
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138 3730774997: 499*997*7499 |
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139 3795321361: 13*37*53^4 |
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140 3877179289: 71^2*877^2 |
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141 4070131949: 13^2*19*31^2*1319 |
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142 4134555661: 41^2*61^2*661 |
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143 4143189277: 31*41^2*43^3 |
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144 4162322419: 19^5*41^2 |
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145 4311603593: 11*43^2*59*3593 |
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146 4339091119: 11*4339*90911 |
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147 4340365711: 11^3*571*5711 |
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148 4375770311: 11^4*31^2*311 |
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149 4427192717: 17*19*71^2*2719 |
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150 4530018503: 503*3001^2 |
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151 4541687137: 13*37*41^3*137 |
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152 4541938631: 41*419^2*631 |
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153 4590757613: 13*613*757*761 |
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154 4750104241: 41^6 |
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155 4796438239: 23^3*479*823 |
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156 4985739599: 59*8573*9857 |
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157 5036760823: 23^3*503*823 |
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158 5094014879: 79*401^3 |
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159 5107117543: 11^4*17^3*71 |
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160 5137905383: 13^2*53^2*79*137 |
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161 5181876331: 31^5*181 |
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162 5276191811: 11^5*181^2 |
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163 5319967909: 19*53^2*99679 |
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164 5411964371: 11*41^2*541^2 |
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165 5445241447: 41^5*47 |
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166 5892813173: 13^3*17^2*9281 |
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167 6021989371: 19^3*937^2 |
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168 6122529619: 19*29^2*619^2 |
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169 6138239333: 23^3*613*823 |
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170 6230438329: 23*29^4*383 |
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171 6612362989: 23^4*23629 |
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172 6645125311: 11^8*31 |
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173 7155432157: 43^2*157^3 |
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174 7232294717: 17*29^2*47^2*229 |
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175 7293289141: 29*41^4*89 |
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176 7491092411: 11*41^4*241 |
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177 8144543377: 433*4337^2 |
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178 8194561699: 19*4561*94561 |
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179 8336743231: 23^4*31^3 |
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180 8413553317: 13*17*53^2*13553 |
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181 8435454179: 17*43^3*79^2 |
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182 8966127229: 29^2*127^2*661 |
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183 9091190911: 11*9091*90911 |
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184 9373076171: 37^2*937*7307 |
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185 9418073141: 31*41^2*180731 |
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186 9419992843: 19^4*41^2*43 |
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187 9523894717: 17^3*23*89*947 |
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188 9898707359: 59^2*89^2*359 |
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runtime 539.800 s |
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</pre> |
</pre> |
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=={{header|Perl}}== |
=={{header|Perl}}== |
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{{trans|Raku}} |
{{trans|Raku}} |
Revision as of 15:53, 21 January 2022
Find the composite numbers k in base 10, that have no single digit prime factors and whose prime factors are all a substring of k.
- Task
- Find and show here, on this page, the first ten elements of the sequence.
- Stretch
- Find and show the next ten elements.
ALGOL 68
<lang algol68>BEGIN # find composite k with no single digit factors whose factors are all substrings of k #
# returns TRUE if the string representation of f is a substring of k str, FALSE otherwise # PROC is substring = ( STRING k str, INT f )BOOL: BEGIN STRING f str = whole( f, 0 ); INT f len = ( UPB f str - LWB f str ) + 1; BOOL result := FALSE; INT f end := ( LWB k str + f len ) - 2; FOR f pos FROM LWB k str TO ( UPB k str + 1 ) - f len WHILE NOT result DO f end +:= 1; result := k str[ f pos : f end ] = f str OD; result END # is substring # ; # task # INT required numbers = 20; INT k count := 0; # k must be odd and > 9 # FOR k FROM 11 BY 2 WHILE k count < required numbers DO IF k MOD 3 /= 0 AND k MOD 5 /= 0 AND k MOD 7 /= 0 THEN # no single digit odd prime factors # BOOL is candidate := TRUE; STRING k str = whole( k, 0 ); INT v := k; INT f count := 0; FOR f FROM 11 BY 2 TO ENTIER sqrt( k ) + 1 WHILE v > 1 AND is candidate DO IF v MOD f = 0 THEN # have a factor # is candidate := is substring( k str, f ); IF is candidate THEN # the digits of f ae a substring of v # WHILE v OVERAB f; f count +:= 1; v MOD f = 0 DO SKIP OD FI FI OD; IF is candidate AND ( f count > 1 OR ( v /= k AND v > 1 ) ) THEN # have a composite whose factors are up to the root are substrings # IF v > 1 THEN # there was a factor > the root # is candidate := is substring( k str, v ) FI; IF is candidate THEN print( ( " ", whole( k, -8 ) ) ); k count +:= 1; IF k count MOD 10 = 0 THEN print( ( newline ) ) FI FI FI FI OD
END</lang>
- Output:
15317 59177 83731 119911 183347 192413 1819231 2111317 2237411 3129361 5526173 11610313 13436683 13731373 13737841 13831103 15813251 17692313 19173071 28118827
Julia
<lang julia>using Lazy using Primes
function containsitsonlytwodigfactors(n)
s = string(n) return !isprime(n) && all(t -> length(t) > 1 && contains(s, t), map(string, collect(keys(factor(n)))))
end
seq = @>> Lazy.range(2) filter(containsitsonlytwodigfactors)
foreach(p -> print(lpad(last(p), 9), first(p) == 10 ? "\n" : ""), enumerate(take(20, seq)))
</lang>
- Output:
15317 59177 83731 119911 183347 192413 1819231 2111317 2237411 3129361 5526173 11610313 13436683 13731373 13737841 13831103 15813251 17692313 19173071 28118827
Pascal
Free Pascal
modified Factors_of_an_integer#using_Prime_decomposition <lang pascal>program FacOfInt; // gets factors of consecutive integers fast // limited to 1.2e11 {$IFDEF FPC}
{$MODE DELPHI} {$OPTIMIZATION ON,ALL} {$COPERATORS ON}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF} uses
sysutils
{$IFDEF WINDOWS},Windows{$ENDIF}
;
//###################################################################### //prime decomposition const //HCN(86) > 1.2E11 = 128,501,493,120 count of divs = 4096 7 3 1 1 1 1 1 1 1
HCN_DivCnt = 4096;
type
tItem = Uint64; tDivisors = array [0..HCN_DivCnt] of tItem; tpDivisor = pUint64;
const
//used odd size for test only SizePrDeFe = 32768;//*72 <= 64kb level I or 2 Mb ~ level 2 cache
type
tdigits = array [0..31] of Uint32; //the first number with 11 different prime factors = //2*3*5*7*11*13*17*19*23*29*31 = 2E11 //56 byte tprimeFac = packed record pfSumOfDivs, pfRemain : Uint64; pfDivCnt : Uint32; pfMaxIdx : Uint32; pfpotPrimIdx : array[0..9] of word; pfpotMax : array[0..11] of byte; end; tpPrimeFac = ^tprimeFac; tPrimeDecompField = array[0..SizePrDeFe-1] of tprimeFac; tPrimes = array[0..65535] of Uint32;
var
{$ALIGN 8} SmallPrimes: tPrimes; {$ALIGN 32} PrimeDecompField :tPrimeDecompField; pdfIDX,pdfOfs: NativeInt;
procedure InitSmallPrimes; //get primes. #0..65535.Sieving only odd numbers const
MAXLIMIT = (821641-1) shr 1;
var
pr : array[0..MAXLIMIT] of byte; p,j,d,flipflop :NativeUInt;
Begin
SmallPrimes[0] := 2; fillchar(pr[0],SizeOf(pr),#0); p := 0; repeat repeat p +=1 until pr[p]= 0; j := (p+1)*p*2; if j>MAXLIMIT then BREAK; d := 2*p+1; repeat pr[j] := 1; j += d; until j>MAXLIMIT; until false; SmallPrimes[1] := 3; SmallPrimes[2] := 5; j := 3; d := 7; flipflop := (2+1)-1;//7+2*2,11+2*1,13,17,19,23 p := 3; repeat if pr[p] = 0 then begin SmallPrimes[j] := d; inc(j); end; d += 2*flipflop; p+=flipflop; flipflop := 3-flipflop; until (p > MAXLIMIT) OR (j>High(SmallPrimes));
end;
function OutPots(pD:tpPrimeFac;n:NativeInt):Ansistring; var
s: String[31]; chk,p,i: NativeInt;
Begin
str(n:12,s); result := s+': '; with pd^ do begin chk := 1; For n := 0 to pfMaxIdx-1 do Begin if n>0 then result += '*'; p := SmallPrimes[pfpotPrimIdx[n]]; chk *= p; str(p,s); result += s; i := pfpotMax[n]; if i >1 then Begin str(pfpotMax[n],s); result += '^'+s; repeat chk *= p; dec(i); until i <= 1; end; end; p := pfRemain; If p >1 then Begin str(p,s); chk *= p; result += '*'+s; end; end;
end;
function CnvtoBASE(var dgt:tDigits;n:Uint64;base:NativeUint):NativeInt; //n must be multiple of base aka n mod base must be 0 var
q,r: Uint64; i : NativeInt;
Begin
fillchar(dgt,SizeOf(dgt),#0); i := 0; n := n div base; result := 0; repeat r := n; q := n div base; r -= q*base; n := q; dgt[i] := r; inc(i); until (q = 0); //searching lowest pot in base result := 0; while (result<i) AND (dgt[result] = 0) do inc(result); inc(result);
end;
function IncByBaseInBase(var dgt:tDigits;base:NativeInt):NativeInt; var
q :NativeInt;
Begin
result := 0; q := dgt[result]+1; if q = base then repeat dgt[result] := 0; inc(result); q := dgt[result]+1; until q <> base; dgt[result] := q; result +=1;
end;
function SieveOneSieve(var pdf:tPrimeDecompField):boolean; var
dgt:tDigits; i,j,k,pr,fac,n,MaxP : Uint64;
begin
n := pdfOfs; if n+SizePrDeFe >= sqr(SmallPrimes[High(SmallPrimes)]) then EXIT(FALSE); //init for i := 0 to SizePrDeFe-1 do begin with pdf[i] do Begin pfDivCnt := 1; pfSumOfDivs := 1; pfRemain := n+i; pfMaxIdx := 0; pfpotPrimIdx[0] := 0; pfpotMax[0] := 0; end; end; //first factor 2. Make n+i even i := (pdfIdx+n) AND 1; IF (n = 0) AND (pdfIdx<2) then i := 2; repeat with pdf[i] do begin j := BsfQWord(n+i); pfMaxIdx := 1; pfpotPrimIdx[0] := 0; pfpotMax[0] := j; pfRemain := (n+i) shr j; pfSumOfDivs := (Uint64(1) shl (j+1))-1; pfDivCnt := j+1; end; i += 2; until i >=SizePrDeFe; //i now index in SmallPrimes i := 0; maxP := trunc(sqrt(n+SizePrDeFe))+1; repeat //search next prime that is in bounds of sieve if n = 0 then begin repeat inc(i); pr := SmallPrimes[i]; k := pr-n MOD pr; if k < SizePrDeFe then break; until pr > MaxP; end else begin repeat inc(i); pr := SmallPrimes[i]; k := pr-n MOD pr; if (k = pr) AND (n>0) then k:= 0; if k < SizePrDeFe then break; until pr > MaxP; end; //no need to use higher primes if pr*pr > n+SizePrDeFe then BREAK; //j is power of prime j := CnvtoBASE(dgt,n+k,pr); repeat with pdf[k] do Begin pfpotPrimIdx[pfMaxIdx] := i; pfpotMax[pfMaxIdx] := j; pfDivCnt *= j+1; fac := pr; repeat pfRemain := pfRemain DIV pr; dec(j); fac *= pr; until j<= 0; pfSumOfDivs *= (fac-1)DIV(pr-1); inc(pfMaxIdx); k += pr; j := IncByBaseInBase(dgt,pr); end; until k >= SizePrDeFe; until false; //correct sum of & count of divisors for i := 0 to High(pdf) do Begin with pdf[i] do begin j := pfRemain; if j <> 1 then begin pfSumOFDivs *= (j+1); pfDivCnt *=2; end; end; end; result := true;
end;
function NextSieve:boolean; begin
dec(pdfIDX,SizePrDeFe); inc(pdfOfs,SizePrDeFe); result := SieveOneSieve(PrimeDecompField);
end;
function GetNextPrimeDecomp:tpPrimeFac; begin
if pdfIDX >= SizePrDeFe then if Not(NextSieve) then EXIT(NIL); result := @PrimeDecompField[pdfIDX]; inc(pdfIDX);
end;
function Init_Sieve(n:NativeUint):boolean; //Init Sieve pdfIdx,pdfOfs are Global begin
pdfIdx := n MOD SizePrDeFe; pdfOfs := n-pdfIdx; result := SieveOneSieve(PrimeDecompField);
end;
var
s,pr : string[31]; pPrimeDecomp :tpPrimeFac; T0:Int64; n,i,cnt : NativeUInt; checked : boolean;
Begin
InitSmallPrimes; T0 := GetTickCount64; cnt := 0; n := 0; Init_Sieve(n); repeat pPrimeDecomp:= GetNextPrimeDecomp; with pPrimeDecomp^ do begin //composite with smallest factor 11 if (pfDivCnt>=4) AND (pfpotPrimIdx[0]>3) then begin str(n,s); for i := 0 to pfMaxIdx-1 do begin str(smallprimes[pfpotPrimIdx[i]],pr); checked := (pos(pr,s)>0); if Not(checked) then Break; end; if checked then begin //writeln(cnt:4,OutPots(pPrimeDecomp,n)); if pfRemain >1 then begin str(pfRemain,pr); checked := (pos(pr,s)>0); end; if checked then begin inc(cnt); writeln(cnt:4,OutPots(pPrimeDecomp,n)); end; end; end; end; inc(n); until n > 28118827;//10*1000*1000*1000+1;// T0 := GetTickCount64-T0; writeln('runtime ',T0/1000:0:3,' s');
end. </lang>
- @TIO.RUN:
Real time: 2.166 s CPU share: 99.20 %//500*1000*1000 Real time: 38.895 s CPU share: 99.28 % 1 15317: 17^2*53 2 59177: 17*59^2 3 83731: 31*37*73 4 119911: 11^2*991 5 183347: 47^2*83 6 192413: 13*19^2*41 7 1819231: 19*23^2*181 8 2111317: 13^3*31^2 9 2237411: 11^3*41^2 10 3129361: 29^2*61^2 11 5526173: 17*61*73^2 12 11610313: 11^4*13*61 13 13436683: 13^2*43^3 14 13731373: 73*137*1373 15 13737841: 13^5*37 16 13831103: 11*13*311^2 17 15813251: 251^3 18 17692313: 23*769231 19 19173071: 19^2*173*307 20 28118827: 11^2*281*827 runtime 2.011 s //@home til 1E10 .. 188 9898707359: 59^2*89^2*359 21 31373137: 73*137*3137 22 47458321: 83^4 23 55251877: 251^2*877 24 62499251: 251*499^2 25 79710361: 103*797*971 26 81227897: 89*97^3 27 97337269: 37^2*97*733 28 103192211: 19^2*31*9221 29 107132311: 11^2*13^4*31 30 119503483: 11*19*83^3 31 119759299: 11*19*29*19759 32 124251499: 499^3 33 131079601: 107^4 34 142153597: 59^2*97*421 35 147008443: 43^5 36 171197531: 17^2*31*97*197 37 179717969: 71*79*179^2 38 183171409: 71*1409*1831 39 215797193: 19*1579*7193 40 241153517: 11*17*241*5351 41 248791373: 73*373*9137 42 261113281: 11^2*13^2*113^2 43 272433191: 19*331*43319 44 277337147: 71*73^2*733 45 291579719: 19*1579*9719 46 312239471: 31^3*47*223 47 344972429: 29*3449^2 48 364181311: 13^4*41*311 49 381317911: 13^6*79 50 385494799: 47^4*79 51 392616923: 23^5*61 52 399311341: 11*13^4*31*41 53 410963311: 11^2*31*331^2 54 413363353: 13^4*41*353 55 423564751: 751^3 56 471751831: 31*47^2*83^2 57 492913739: 73*739*9137 58 501225163: 163*251*12251 59 591331169: 11*13^2*31^2*331 60 592878929: 29^2*89^3 61 594391193: 11*19^2*43*59^2 62 647959343: 47^3*79^2 63 717528911: 11^2*17^4*71 64 723104383: 23^2*43*83*383 65 772253089: 53^2*89*3089 66 799216219: 79^3*1621 67 847253389: 53^2*89*3389 68 889253557: 53^2*89*3557 69 889753559: 53^2*89*3559 70 892753571: 53^2*89*3571 71 892961737: 17^2*37^3*61 72 895253581: 53^2*89*3581 73 895753583: 53^2*89*3583 74 898253593: 53^2*89*3593 75 972253889: 53^2*89*3889 76 997253989: 53^2*89*3989 77 1005371999: 53^2*71^3 78 1011819919: 11*101*919*991 79 1019457337: 37^2*73*101^2 80 1029761609: 29^2*761*1609 81 1031176157: 11^2*17*31*103*157 82 1109183317: 11*31^2*317*331 83 1119587711: 11^2*19^4*71 84 1137041971: 13^4*41*971 85 1158169331: 11*31^2*331^2 86 1161675547: 47^3*67*167 87 1189683737: 11^5*83*89 88 1190911909: 11*9091*11909 89 1193961571: 11^3*571*1571 90 1274418211: 11*41^5 91 1311979279: 13^2*19*131*3119 92 1316779217: 13^2*17*677^2 93 1334717327: 47*73^4 94 1356431947: 13*43^2*56431 95 1363214333: 13^3*433*1433 96 1371981127: 11^2*19*37*127^2 97 1379703847: 47^3*97*137 98 1382331137: 11*31*37*331^2 99 1389214193: 41*193*419^2 100 1497392977: 97*3929^2 101 1502797333: 733^2*2797 102 1583717977: 17^2*71*79*977 103 1593519731: 59*5197^2 104 1713767399: 17^6*71 105 1729719587: 17*19^2*29*9719 106 1733793487: 79^2*379*733 107 1761789373: 17^2*37^2*61*73 108 1871688013: 13^5*71^2 109 1907307719: 71^3*73^2 110 1948441249: 1249^3 111 1963137527: 13*31^3*37*137 112 1969555417: 17*41^5 113 1982119441: 211^4 114 1997841197: 11*97^3*199 115 2043853681: 53^2*853^2 116 2070507919: 19^2*79^2*919 117 2073071593: 73^5 118 2278326179: 17*83*617*2617 119 2297126743: 29^3*97*971 120 2301131209: 13^4*23*31*113 121 2323519823: 19^2*23^5 122 2371392959: 13^2*29*59^2*139 123 2647985311: 31*47*53^2*647 124 2667165611: 11^5*16561 125 2722413361: 241*3361^2 126 2736047519: 19^2*47^3*73 127 2881415311: 31^3*311^2 128 2911317539: 13^2*31*317*1753 129 2924190611: 19^3*29*61*241 130 3015962419: 41*419^3 131 3112317013: 13^2*23^2*31*1123 132 3131733761: 13^2*17^2*37*1733 133 3150989441: 41*509*150989 134 3151811881: 31^2*1811^2 135 3423536177: 17*23^2*617^2 136 3461792569: 17^2*3461^2 137 3559281161: 281*3559^2 138 3730774997: 499*997*7499 139 3795321361: 13*37*53^4 140 3877179289: 71^2*877^2 141 4070131949: 13^2*19*31^2*1319 142 4134555661: 41^2*61^2*661 143 4143189277: 31*41^2*43^3 144 4162322419: 19^5*41^2 145 4311603593: 11*43^2*59*3593 146 4339091119: 11*4339*90911 147 4340365711: 11^3*571*5711 148 4375770311: 11^4*31^2*311 149 4427192717: 17*19*71^2*2719 150 4530018503: 503*3001^2 151 4541687137: 13*37*41^3*137 152 4541938631: 41*419^2*631 153 4590757613: 13*613*757*761 154 4750104241: 41^6 155 4796438239: 23^3*479*823 156 4985739599: 59*8573*9857 157 5036760823: 23^3*503*823 158 5094014879: 79*401^3 159 5107117543: 11^4*17^3*71 160 5137905383: 13^2*53^2*79*137 161 5181876331: 31^5*181 162 5276191811: 11^5*181^2 163 5319967909: 19*53^2*99679 164 5411964371: 11*41^2*541^2 165 5445241447: 41^5*47 166 5892813173: 13^3*17^2*9281 167 6021989371: 19^3*937^2 168 6122529619: 19*29^2*619^2 169 6138239333: 23^3*613*823 170 6230438329: 23*29^4*383 171 6612362989: 23^4*23629 172 6645125311: 11^8*31 173 7155432157: 43^2*157^3 174 7232294717: 17*29^2*47^2*229 175 7293289141: 29*41^4*89 176 7491092411: 11*41^4*241 177 8144543377: 433*4337^2 178 8194561699: 19*4561*94561 179 8336743231: 23^4*31^3 180 8413553317: 13*17*53^2*13553 181 8435454179: 17*43^3*79^2 182 8966127229: 29^2*127^2*661 183 9091190911: 11*9091*90911 184 9373076171: 37^2*937*7307 185 9418073141: 31*41^2*180731 186 9419992843: 19^4*41^2*43 187 9523894717: 17^3*23*89*947 188 9898707359: 59^2*89^2*359 runtime 539.800 s
Perl
<lang perl> use strict; use warnings; use ntheory qw<is_prime factor gcd>;
my($values,$cnt); LOOP: for (my $k = 11; $k < 1E10; $k += 2) {
next if 1 < gcd($k,2*3*5*7) or is_prime $k; map { next if index($k, $_) < 0 } factor $k; $values .= sprintf "%10d", $k; last LOOP if ++$cnt == 20;
} print $values =~ s/.{1,100}\K/\n/gr;</lang>
- Output:
15317 59177 83731 119911 183347 192413 1819231 2111317 2237411 3129361 5526173 11610313 13436683 13731373 13737841 13831103 15813251 17692313 19173071 28118827
Phix
with javascript_semantics integer count = 0, n = 11*11, limit = iff(platform()=JS?10:20) atom t0 = time(), t1 = time() while count<limit do if gcd(n,3*5*7)=1 then sequence f = prime_factors(n,true,-1) if length(f)>1 then string s = sprintf("%d",n) bool valid = true for i=1 to length(f) do if (i=1 or f[i]!=f[i-1]) and not match(sprintf("%d",f[i]),s) then valid = false exit end if end for if valid then count += 1 string t = join(apply(f,sprint),"x"), e = elapsed(time()-t1) printf(1,"%2d: %,10d = %-17s (%s)\n",{count,n,t,e}) t1 = time() end if end if end if n += 2 end while printf(1,"Total time:%s\n",{elapsed(time()-t0)})
- Output:
(As usual, limiting to the first 10 under pwa/p2js keeps the time staring at a blank screen under 10s)
1: 15,317 = 17x17x53 (0s) 2: 59,177 = 17x59x59 (0.1s) 3: 83,731 = 31x37x73 (0.0s) 4: 119,911 = 11x11x991 (0.0s) 5: 183,347 = 47x47x83 (0.1s) 6: 192,413 = 13x19x19x41 (0.0s) 7: 1,819,231 = 19x23x23x181 (3.5s) 8: 2,111,317 = 13x13x13x31x31 (0.7s) 9: 2,237,411 = 11x11x11x41x41 (0.4s) 10: 3,129,361 = 29x29x61x61 (2.6s) 11: 5,526,173 = 17x61x73x73 (7.5s) 12: 11,610,313 = 11x11x11x11x13x61 (23.2s) 13: 13,436,683 = 13x13x43x43x43 (7.9s) 14: 13,731,373 = 73x137x1373 (1.3s) 15: 13,737,841 = 13x13x13x13x13x37 (0.0s) 16: 13,831,103 = 11x13x311x311 (0.4s) 17: 15,813,251 = 251x251x251 (8.9s) 18: 17,692,313 = 23x769231 (9.0s) 19: 19,173,071 = 19x19x173x307 (7.1s) 20: 28,118,827 = 11x11x281x827 (46.2s) Total time:1 minute and 59s
Raku
<lang perl6>use Prime::Factor; use Lingua::EN::Numbers;
put (2..∞).hyper(:5000batch).map( {
next if (1 < $_ gcd 210) || .is-prime || any .&prime-factors.map: -> $n { !.contains: $n }; $_
} )[^20].batch(10)».&comma».fmt("%10s").join: "\n";</lang>
- Output:
15,317 59,177 83,731 119,911 183,347 192,413 1,819,231 2,111,317 2,237,411 3,129,361 5,526,173 11,610,313 13,436,683 13,731,373 13,737,841 13,831,103 15,813,251 17,692,313 19,173,071 28,118,827
Wren
<lang ecmascript>import "/math" for Int import "/seq" for Lst import "/fmt" for Fmt
var count = 0 var k = 11 * 11 var res = [] while (count < 20) {
if (k % 3 == 0 || k % 5 == 0 || k % 7 == 0) { k = k + 2 continue } var factors = Int.primeFactors(k) if (factors.count > 1) { Lst.prune(factors) var s = k.toString var includesAll = true for (f in factors) { if (s.indexOf(f.toString) == -1) { includesAll = false break } } if (includesAll) { res.add(k) count = count + 1 } } k = k + 2
} Fmt.print("$,10d", res[0..9]) Fmt.print("$,10d", res[10..19])</lang>
- Output:
15,317 59,177 83,731 119,911 183,347 192,413 1,819,231 2,111,317 2,237,411 3,129,361 5,526,173 11,610,313 13,436,683 13,731,373 13,737,841 13,831,103 15,813,251 17,692,313 19,173,071 28,118,827