All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Induced divisibility (Posted on 2021-03-18) Difficulty: 3 of 5
There is some natural number written on the board. An operation is defined as adding to the number its maximal proper divisor. Prove that after some iterations of this operation that we get a number that's divisible by 32020.

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts a pattern | Comment 4 of 7 |
Any number seems to quickly settle into a pattern of gaining a power of 3 for every third iteration of the operation:

digits(400)
clc
for n0=7:16
pow3=vpa(3); p3=1; iter=1;
n=vpa(n0);
disp(n0)
while pow3<vpa(9999999999999999)
    nTrial=n;
    while mod(nTrial,pow3)==0
       disp([n iter p3 pow3 n/pow3])
       pow3=3*pow3; p3=p3+1;
    end
    f=factor(n);
    n=n+n/f(1); iter=iter+1;
end
end

The results show the starting number followed by lines which show successive iteration numbers that achieve a given power of 3.  Each line shows first the number achieved at that number of iterations; second, the number of iterations at that point; third, the power of 3; fourth, the value of that power of 3; and finally, the multiple of 3^2020 that the value is.


     7
[ 12.0, 3, 1, 3.0, 4.0]
[ 18.0, 4, 2, 9.0, 2.0]
[ 27.0, 5, 3, 27.0, 1.0]
[ 81.0, 8, 4, 81.0, 1.0]
[ 243.0, 11, 5, 243.0, 1.0]
[ 729.0, 14, 6, 729.0, 1.0]
[ 2187.0, 17, 7, 2187.0, 1.0]
[ 6561.0, 20, 8, 6561.0, 1.0]
[ 19683.0, 23, 9, 19683.0, 1.0]
[ 59049.0, 26, 10, 59049.0, 1.0]
[ 177147.0, 29, 11, 177147.0, 1.0]
[ 531441.0, 32, 12, 531441.0, 1.0]
[ 1594323.0, 35, 13, 1594323.0, 1.0]
[ 4782969.0, 38, 14, 4782969.0, 1.0]
[ 14348907.0, 41, 15, 14348907.0, 1.0]
[ 43046721.0, 44, 16, 43046721.0, 1.0]
[ 129140163.0, 47, 17, 129140163.0, 1.0]
[ 387420489.0, 50, 18, 387420489.0, 1.0]
[ 1162261467.0, 53, 19, 1162261467.0, 1.0]
[ 3486784401.0, 56, 20, 3486784401.0, 1.0]
[ 10460353203.0, 59, 21, 10460353203.0, 1.0]
[ 31381059609.0, 62, 22, 31381059609.0, 1.0]
[ 94143178827.0, 65, 23, 94143178827.0, 1.0]
[ 282429536481.0, 68, 24, 282429536481.0, 1.0]
[ 847288609443.0, 71, 25, 847288609443.0, 1.0]
[ 2541865828329.0, 74, 26, 2541865828329.0, 1.0]
[ 7625597484987.0, 77, 27, 7625597484987.0, 1.0]
[ 22876792454961.0, 80, 28, 22876792454961.0, 1.0]
[ 68630377364883.0, 83, 29, 68630377364883.0, 1.0]
[ 205891132094649.0, 86, 30, 205891132094649.0, 1.0]
[ 617673396283947.0, 89, 31, 617673396283947.0, 1.0]
[ 1853020188851841.0, 92, 32, 1853020188851841.0, 1.0]
[ 5559060566555523.0, 95, 33, 5559060566555523.0, 1.0]
     8
[ 12.0, 2, 1, 3.0, 4.0]
[ 18.0, 3, 2, 9.0, 2.0]
[ 27.0, 4, 3, 27.0, 1.0]
[ 81.0, 7, 4, 81.0, 1.0]
[ 243.0, 10, 5, 243.0, 1.0]
[ 729.0, 13, 6, 729.0, 1.0]
[ 2187.0, 16, 7, 2187.0, 1.0]
[ 6561.0, 19, 8, 6561.0, 1.0]
[ 19683.0, 22, 9, 19683.0, 1.0]
[ 59049.0, 25, 10, 59049.0, 1.0]
[ 177147.0, 28, 11, 177147.0, 1.0]
[ 531441.0, 31, 12, 531441.0, 1.0]
[ 1594323.0, 34, 13, 1594323.0, 1.0]
[ 4782969.0, 37, 14, 4782969.0, 1.0]
[ 14348907.0, 40, 15, 14348907.0, 1.0]
[ 43046721.0, 43, 16, 43046721.0, 1.0]
[ 129140163.0, 46, 17, 129140163.0, 1.0]
[ 387420489.0, 49, 18, 387420489.0, 1.0]
[ 1162261467.0, 52, 19, 1162261467.0, 1.0]
[ 3486784401.0, 55, 20, 3486784401.0, 1.0]
[ 10460353203.0, 58, 21, 10460353203.0, 1.0]
[ 31381059609.0, 61, 22, 31381059609.0, 1.0]
[ 94143178827.0, 64, 23, 94143178827.0, 1.0]
[ 282429536481.0, 67, 24, 282429536481.0, 1.0]
[ 847288609443.0, 70, 25, 847288609443.0, 1.0]
[ 2541865828329.0, 73, 26, 2541865828329.0, 1.0]
[ 7625597484987.0, 76, 27, 7625597484987.0, 1.0]
[ 22876792454961.0, 79, 28, 22876792454961.0, 1.0]
[ 68630377364883.0, 82, 29, 68630377364883.0, 1.0]
[ 205891132094649.0, 85, 30, 205891132094649.0, 1.0]
[ 617673396283947.0, 88, 31, 617673396283947.0, 1.0]
[ 1853020188851841.0, 91, 32, 1853020188851841.0, 1.0]
[ 5559060566555523.0, 94, 33, 5559060566555523.0, 1.0]
     9
[ 9.0, 1, 1, 3.0, 3.0]
[ 9.0, 1, 2, 9.0, 1.0]
[ 27.0, 4, 3, 27.0, 1.0]
[ 81.0, 7, 4, 81.0, 1.0]
[ 243.0, 10, 5, 243.0, 1.0]
[ 729.0, 13, 6, 729.0, 1.0]
[ 2187.0, 16, 7, 2187.0, 1.0]
[ 6561.0, 19, 8, 6561.0, 1.0]
[ 19683.0, 22, 9, 19683.0, 1.0]
[ 59049.0, 25, 10, 59049.0, 1.0]
[ 177147.0, 28, 11, 177147.0, 1.0]
[ 531441.0, 31, 12, 531441.0, 1.0]
[ 1594323.0, 34, 13, 1594323.0, 1.0]
[ 4782969.0, 37, 14, 4782969.0, 1.0]
[ 14348907.0, 40, 15, 14348907.0, 1.0]
[ 43046721.0, 43, 16, 43046721.0, 1.0]
[ 129140163.0, 46, 17, 129140163.0, 1.0]
[ 387420489.0, 49, 18, 387420489.0, 1.0]
[ 1162261467.0, 52, 19, 1162261467.0, 1.0]
[ 3486784401.0, 55, 20, 3486784401.0, 1.0]
[ 10460353203.0, 58, 21, 10460353203.0, 1.0]
[ 31381059609.0, 61, 22, 31381059609.0, 1.0]
[ 94143178827.0, 64, 23, 94143178827.0, 1.0]
[ 282429536481.0, 67, 24, 282429536481.0, 1.0]
[ 847288609443.0, 70, 25, 847288609443.0, 1.0]
[ 2541865828329.0, 73, 26, 2541865828329.0, 1.0]
[ 7625597484987.0, 76, 27, 7625597484987.0, 1.0]
[ 22876792454961.0, 79, 28, 22876792454961.0, 1.0]
[ 68630377364883.0, 82, 29, 68630377364883.0, 1.0]
[ 205891132094649.0, 85, 30, 205891132094649.0, 1.0]
[ 617673396283947.0, 88, 31, 617673396283947.0, 1.0]
[ 1853020188851841.0, 91, 32, 1853020188851841.0, 1.0]
[ 5559060566555523.0, 94, 33, 5559060566555523.0, 1.0]
    10
[ 15.0, 2, 1, 3.0, 5.0]
[ 45.0, 5, 2, 9.0, 5.0]
[ 135.0, 8, 3, 27.0, 5.0]
[ 405.0, 11, 4, 81.0, 5.0]
[ 1215.0, 14, 5, 243.0, 5.0]
[ 3645.0, 17, 6, 729.0, 5.0]
[ 10935.0, 20, 7, 2187.0, 5.0]
[ 32805.0, 23, 8, 6561.0, 5.0]
[ 98415.0, 26, 9, 19683.0, 5.0]
[ 295245.0, 29, 10, 59049.0, 5.0]
[ 885735.0, 32, 11, 177147.0, 5.0]
[ 2657205.0, 35, 12, 531441.0, 5.0]
[ 7971615.0, 38, 13, 1594323.0, 5.0]
[ 23914845.0, 41, 14, 4782969.0, 5.0]
[ 71744535.0, 44, 15, 14348907.0, 5.0]
[ 215233605.0, 47, 16, 43046721.0, 5.0]
[ 645700815.0, 50, 17, 129140163.0, 5.0]
[ 1937102445.0, 53, 18, 387420489.0, 5.0]
[ 5811307335.0, 56, 19, 1162261467.0, 5.0]
[ 17433922005.0, 59, 20, 3486784401.0, 5.0]
[ 52301766015.0, 62, 21, 10460353203.0, 5.0]
[ 156905298045.0, 65, 22, 31381059609.0, 5.0]
[ 470715894135.0, 68, 23, 94143178827.0, 5.0]
[ 1412147682405.0, 71, 24, 282429536481.0, 5.0]
[ 4236443047215.0, 74, 25, 847288609443.0, 5.0]
[ 12709329141645.0, 77, 26, 2541865828329.0, 5.0]
[ 38127987424935.0, 80, 27, 7625597484987.0, 5.0]
[ 114383962274805.0, 83, 28, 22876792454961.0, 5.0]
[ 343151886824415.0, 86, 29, 68630377364883.0, 5.0]
[ 1029455660473245.0, 89, 30, 205891132094649.0, 5.0]

    11
[ 12.0, 2, 1, 3.0, 4.0]
[ 18.0, 3, 2, 9.0, 2.0]
[ 27.0, 4, 3, 27.0, 1.0]
[ 81.0, 7, 4, 81.0, 1.0]
[ 243.0, 10, 5, 243.0, 1.0]
[ 729.0, 13, 6, 729.0, 1.0]
[ 2187.0, 16, 7, 2187.0, 1.0]
[ 6561.0, 19, 8, 6561.0, 1.0]
[ 19683.0, 22, 9, 19683.0, 1.0]
[ 59049.0, 25, 10, 59049.0, 1.0]
[ 177147.0, 28, 11, 177147.0, 1.0]
[ 531441.0, 31, 12, 531441.0, 1.0]
[ 1594323.0, 34, 13, 1594323.0, 1.0]
[ 4782969.0, 37, 14, 4782969.0, 1.0]
[ 14348907.0, 40, 15, 14348907.0, 1.0]
[ 43046721.0, 43, 16, 43046721.0, 1.0]
[ 129140163.0, 46, 17, 129140163.0, 1.0]
[ 387420489.0, 49, 18, 387420489.0, 1.0]
[ 1162261467.0, 52, 19, 1162261467.0, 1.0]
[ 3486784401.0, 55, 20, 3486784401.0, 1.0]
[ 10460353203.0, 58, 21, 10460353203.0, 1.0]
[ 31381059609.0, 61, 22, 31381059609.0, 1.0]
[ 94143178827.0, 64, 23, 94143178827.0, 1.0]
[ 282429536481.0, 67, 24, 282429536481.0, 1.0]
[ 847288609443.0, 70, 25, 847288609443.0, 1.0]
[ 2541865828329.0, 73, 26, 2541865828329.0, 1.0]
[ 7625597484987.0, 76, 27, 7625597484987.0, 1.0]
[ 22876792454961.0, 79, 28, 22876792454961.0, 1.0]
[ 68630377364883.0, 82, 29, 68630377364883.0, 1.0]
[ 205891132094649.0, 85, 30, 205891132094649.0, 1.0]
[ 617673396283947.0, 88, 31, 617673396283947.0, 1.0]
[ 1853020188851841.0, 91, 32, 1853020188851841.0, 1.0]
[ 5559060566555523.0, 94, 33, 5559060566555523.0, 1.0]
    12
[ 12.0, 1, 1, 3.0, 4.0]
[ 18.0, 2, 2, 9.0, 2.0]
[ 27.0, 3, 3, 27.0, 1.0]
[ 81.0, 6, 4, 81.0, 1.0]
[ 243.0, 9, 5, 243.0, 1.0]
[ 729.0, 12, 6, 729.0, 1.0]
[ 2187.0, 15, 7, 2187.0, 1.0]
[ 6561.0, 18, 8, 6561.0, 1.0]
[ 19683.0, 21, 9, 19683.0, 1.0]
[ 59049.0, 24, 10, 59049.0, 1.0]
[ 177147.0, 27, 11, 177147.0, 1.0]
[ 531441.0, 30, 12, 531441.0, 1.0]
[ 1594323.0, 33, 13, 1594323.0, 1.0]
[ 4782969.0, 36, 14, 4782969.0, 1.0]
[ 14348907.0, 39, 15, 14348907.0, 1.0]
[ 43046721.0, 42, 16, 43046721.0, 1.0]
[ 129140163.0, 45, 17, 129140163.0, 1.0]
[ 387420489.0, 48, 18, 387420489.0, 1.0]
[ 1162261467.0, 51, 19, 1162261467.0, 1.0]
[ 3486784401.0, 54, 20, 3486784401.0, 1.0]
[ 10460353203.0, 57, 21, 10460353203.0, 1.0]
[ 31381059609.0, 60, 22, 31381059609.0, 1.0]
[ 94143178827.0, 63, 23, 94143178827.0, 1.0]
[ 282429536481.0, 66, 24, 282429536481.0, 1.0]
[ 847288609443.0, 69, 25, 847288609443.0, 1.0]
[ 2541865828329.0, 72, 26, 2541865828329.0, 1.0]
[ 7625597484987.0, 75, 27, 7625597484987.0, 1.0]
[ 22876792454961.0, 78, 28, 22876792454961.0, 1.0]
[ 68630377364883.0, 81, 29, 68630377364883.0, 1.0]
[ 205891132094649.0, 84, 30, 205891132094649.0, 1.0]
[ 617673396283947.0, 87, 31, 617673396283947.0, 1.0]
[ 1853020188851841.0, 90, 32, 1853020188851841.0, 1.0]
[ 5559060566555523.0, 93, 33, 5559060566555523.0, 1.0]
    13
[ 21.0, 3, 1, 3.0, 7.0]
[ 63.0, 6, 2, 9.0, 7.0]
[ 189.0, 9, 3, 27.0, 7.0]
[ 567.0, 12, 4, 81.0, 7.0]
[ 1701.0, 15, 5, 243.0, 7.0]
[ 5103.0, 18, 6, 729.0, 7.0]
[ 15309.0, 21, 7, 2187.0, 7.0]
[ 45927.0, 24, 8, 6561.0, 7.0]
[ 137781.0, 27, 9, 19683.0, 7.0]
[ 413343.0, 30, 10, 59049.0, 7.0]
[ 1240029.0, 33, 11, 177147.0, 7.0]
[ 3720087.0, 36, 12, 531441.0, 7.0]
[ 11160261.0, 39, 13, 1594323.0, 7.0]
[ 33480783.0, 42, 14, 4782969.0, 7.0]
[ 100442349.0, 45, 15, 14348907.0, 7.0]
[ 301327047.0, 48, 16, 43046721.0, 7.0]
[ 903981141.0, 51, 17, 129140163.0, 7.0]
[ 2711943423.0, 54, 18, 387420489.0, 7.0]
[ 8135830269.0, 57, 19, 1162261467.0, 7.0]
[ 24407490807.0, 60, 20, 3486784401.0, 7.0]
[ 73222472421.0, 63, 21, 10460353203.0, 7.0]
[ 219667417263.0, 66, 22, 31381059609.0, 7.0]
[ 659002251789.0, 69, 23, 94143178827.0, 7.0]
[ 1977006755367.0, 72, 24, 282429536481.0, 7.0]
[ 5931020266101.0, 75, 25, 847288609443.0, 7.0]
[ 17793060798303.0, 78, 26, 2541865828329.0, 7.0]
[ 53379182394909.0, 81, 27, 7625597484987.0, 7.0]
[ 160137547184727.0, 84, 28, 22876792454961.0, 7.0]
[ 480412641554181.0, 87, 29, 68630377364883.0, 7.0]
[ 1441237924662543.0, 90, 30, 205891132094649.0, 7.0]
[ 4323713773987629.0, 93, 31, 617673396283947.0, 7.0]
[ 12971141321962887.0, 96, 32, 1853020188851841.0, 7.0]
[ 38913423965888661.0, 99, 33, 5559060566555523.0, 7.0]
    14
[ 21.0, 2, 1, 3.0, 7.0]
[ 63.0, 5, 2, 9.0, 7.0]
[ 189.0, 8, 3, 27.0, 7.0]
[ 567.0, 11, 4, 81.0, 7.0]
[ 1701.0, 14, 5, 243.0, 7.0]
[ 5103.0, 17, 6, 729.0, 7.0]
[ 15309.0, 20, 7, 2187.0, 7.0]
[ 45927.0, 23, 8, 6561.0, 7.0]
[ 137781.0, 26, 9, 19683.0, 7.0]
[ 413343.0, 29, 10, 59049.0, 7.0]
[ 1240029.0, 32, 11, 177147.0, 7.0]
[ 3720087.0, 35, 12, 531441.0, 7.0]
[ 11160261.0, 38, 13, 1594323.0, 7.0]
[ 33480783.0, 41, 14, 4782969.0, 7.0]
[ 100442349.0, 44, 15, 14348907.0, 7.0]
[ 301327047.0, 47, 16, 43046721.0, 7.0]
[ 903981141.0, 50, 17, 129140163.0, 7.0]
[ 2711943423.0, 53, 18, 387420489.0, 7.0]
[ 8135830269.0, 56, 19, 1162261467.0, 7.0]
[ 24407490807.0, 59, 20, 3486784401.0, 7.0]
[ 73222472421.0, 62, 21, 10460353203.0, 7.0]
[ 219667417263.0, 65, 22, 31381059609.0, 7.0]
[ 659002251789.0, 68, 23, 94143178827.0, 7.0]
[ 1977006755367.0, 71, 24, 282429536481.0, 7.0]
[ 5931020266101.0, 74, 25, 847288609443.0, 7.0]
[ 17793060798303.0, 77, 26, 2541865828329.0, 7.0]
[ 53379182394909.0, 80, 27, 7625597484987.0, 7.0]
[ 160137547184727.0, 83, 28, 22876792454961.0, 7.0]
[ 480412641554181.0, 86, 29, 68630377364883.0, 7.0]
[ 1441237924662543.0, 89, 30, 205891132094649.0, 7.0]
[ 4323713773987629.0, 92, 31, 617673396283947.0, 7.0]
[ 12971141321962887.0, 95, 32, 1853020188851841.0, 7.0]
[ 38913423965888661.0, 98, 33, 5559060566555523.0, 7.0]
    15
[ 15.0, 1, 1, 3.0, 5.0]
[ 45.0, 4, 2, 9.0, 5.0]
[ 135.0, 7, 3, 27.0, 5.0]
[ 405.0, 10, 4, 81.0, 5.0]
[ 1215.0, 13, 5, 243.0, 5.0]
[ 3645.0, 16, 6, 729.0, 5.0]
[ 10935.0, 19, 7, 2187.0, 5.0]
[ 32805.0, 22, 8, 6561.0, 5.0]
[ 98415.0, 25, 9, 19683.0, 5.0]
[ 295245.0, 28, 10, 59049.0, 5.0]
[ 885735.0, 31, 11, 177147.0, 5.0]
[ 2657205.0, 34, 12, 531441.0, 5.0]
[ 7971615.0, 37, 13, 1594323.0, 5.0]
[ 23914845.0, 40, 14, 4782969.0, 5.0]
[ 71744535.0, 43, 15, 14348907.0, 5.0]
[ 215233605.0, 46, 16, 43046721.0, 5.0]
[ 645700815.0, 49, 17, 129140163.0, 5.0]
[ 1937102445.0, 52, 18, 387420489.0, 5.0]
[ 5811307335.0, 55, 19, 1162261467.0, 5.0]
[ 17433922005.0, 58, 20, 3486784401.0, 5.0]
[ 52301766015.0, 61, 21, 10460353203.0, 5.0]
[ 156905298045.0, 64, 22, 31381059609.0, 5.0]
[ 470715894135.0, 67, 23, 94143178827.0, 5.0]
[ 1412147682405.0, 70, 24, 282429536481.0, 5.0]
[ 4236443047215.0, 73, 25, 847288609443.0, 5.0]
[ 12709329141645.0, 76, 26, 2541865828329.0, 5.0]
[ 38127987424935.0, 79, 27, 7625597484987.0, 5.0]
[ 114383962274805.0, 82, 28, 22876792454961.0, 5.0]
[ 343151886824415.0, 85, 29, 68630377364883.0, 5.0]
[ 1029455660473245.0, 88, 30, 205891132094649.0, 5.0]
[ 3088366981419735.0, 91, 31, 617673396283947.0, 5.0]
[ 9265100944259205.0, 94, 32, 1853020188851841.0, 5.0]
[ 27795302832777615.0, 97, 33, 5559060566555523.0, 5.0]
    16
[ 24.0, 2, 1, 3.0, 8.0]
[ 36.0, 3, 2, 9.0, 4.0]
[ 54.0, 4, 3, 27.0, 2.0]
[ 81.0, 5, 4, 81.0, 1.0]
[ 243.0, 8, 5, 243.0, 1.0]
[ 729.0, 11, 6, 729.0, 1.0]
[ 2187.0, 14, 7, 2187.0, 1.0]
[ 6561.0, 17, 8, 6561.0, 1.0]
[ 19683.0, 20, 9, 19683.0, 1.0]
[ 59049.0, 23, 10, 59049.0, 1.0]
[ 177147.0, 26, 11, 177147.0, 1.0]
[ 531441.0, 29, 12, 531441.0, 1.0]
[ 1594323.0, 32, 13, 1594323.0, 1.0]
[ 4782969.0, 35, 14, 4782969.0, 1.0]
[ 14348907.0, 38, 15, 14348907.0, 1.0]
[ 43046721.0, 41, 16, 43046721.0, 1.0]
[ 129140163.0, 44, 17, 129140163.0, 1.0]
[ 387420489.0, 47, 18, 387420489.0, 1.0]
[ 1162261467.0, 50, 19, 1162261467.0, 1.0]
[ 3486784401.0, 53, 20, 3486784401.0, 1.0]
[ 10460353203.0, 56, 21, 10460353203.0, 1.0]
[ 31381059609.0, 59, 22, 31381059609.0, 1.0]
[ 94143178827.0, 62, 23, 94143178827.0, 1.0]
[ 282429536481.0, 65, 24, 282429536481.0, 1.0]
[ 847288609443.0, 68, 25, 847288609443.0, 1.0]
[ 2541865828329.0, 71, 26, 2541865828329.0, 1.0]
[ 7625597484987.0, 74, 27, 7625597484987.0, 1.0]
[ 22876792454961.0, 77, 28, 22876792454961.0, 1.0]
[ 68630377364883.0, 80, 29, 68630377364883.0, 1.0]
[ 205891132094649.0, 83, 30, 205891132094649.0, 1.0]
[ 617673396283947.0, 86, 31, 617673396283947.0, 1.0]
[ 1853020188851841.0, 89, 32, 1853020188851841.0, 1.0]
[ 5559060566555523.0, 92, 33, 5559060566555523.0, 1.0]
>> 
   101
[ 102.0, 2, 1, 3.0, 34.0]
[ 153.0, 3, 2, 9.0, 17.0]
[ 459.0, 6, 3, 27.0, 17.0]
[ 1377.0, 9, 4, 81.0, 17.0]
[ 4131.0, 12, 5, 243.0, 17.0]
[ 12393.0, 15, 6, 729.0, 17.0]
[ 37179.0, 18, 7, 2187.0, 17.0]
[ 111537.0, 21, 8, 6561.0, 17.0]
[ 334611.0, 24, 9, 19683.0, 17.0]
[ 1003833.0, 27, 10, 59049.0, 17.0]
[ 3011499.0, 30, 11, 177147.0, 17.0]
[ 9034497.0, 33, 12, 531441.0, 17.0]
[ 27103491.0, 36, 13, 1594323.0, 17.0]
[ 81310473.0, 39, 14, 4782969.0, 17.0]
[ 243931419.0, 42, 15, 14348907.0, 17.0]
[ 731794257.0, 45, 16, 43046721.0, 17.0]
[ 2195382771.0, 48, 17, 129140163.0, 17.0]
[ 6586148313.0, 51, 18, 387420489.0, 17.0]
[ 19758444939.0, 54, 19, 1162261467.0, 17.0]
[ 59275334817.0, 57, 20, 3486784401.0, 17.0]
[ 177826004451.0, 60, 21, 10460353203.0, 17.0]
[ 533478013353.0, 63, 22, 31381059609.0, 17.0]
[ 1600434040059.0, 66, 23, 94143178827.0, 17.0]
   231
[ 231.0, 1, 1, 3.0, 77.0]
[ 693.0, 4, 2, 9.0, 77.0]
[ 2079.0, 7, 3, 27.0, 77.0]
[ 6237.0, 10, 4, 81.0, 77.0]
[ 18711.0, 13, 5, 243.0, 77.0]
[ 56133.0, 16, 6, 729.0, 77.0]
[ 168399.0, 19, 7, 2187.0, 77.0]
[ 505197.0, 22, 8, 6561.0, 77.0]
[ 1515591.0, 25, 9, 19683.0, 77.0]
[ 4546773.0, 28, 10, 59049.0, 77.0]
[ 13640319.0, 31, 11, 177147.0, 77.0]
[ 40920957.0, 34, 12, 531441.0, 77.0]
[ 122762871.0, 37, 13, 1594323.0, 77.0]
[ 368288613.0, 40, 14, 4782969.0, 77.0]
[ 1104865839.0, 43, 15, 14348907.0, 77.0]
[ 3314597517.0, 46, 16, 43046721.0, 77.0]
[ 9943792551.0, 49, 17, 129140163.0, 77.0]
[ 29831377653.0, 52, 18, 387420489.0, 77.0]
[ 89494132959.0, 55, 19, 1162261467.0, 77.0]
[ 268482398877.0, 58, 20, 3486784401.0, 77.0]
[ 805447196631.0, 61, 21, 10460353203.0, 77.0]
[ 2416341589893.0, 64, 22, 31381059609.0, 77.0]
[ 7249024769679.0, 67, 23, 94143178827.0, 77.0]
   500
[ 750.0, 2, 1, 3.0, 250.0]
[ 1125.0, 3, 2, 9.0, 125.0]
[ 3375.0, 6, 3, 27.0, 125.0]
[ 10125.0, 9, 4, 81.0, 125.0]
[ 30375.0, 12, 5, 243.0, 125.0]
[ 91125.0, 15, 6, 729.0, 125.0]
[ 273375.0, 18, 7, 2187.0, 125.0]
[ 820125.0, 21, 8, 6561.0, 125.0]
[ 2460375.0, 24, 9, 19683.0, 125.0]
[ 7381125.0, 27, 10, 59049.0, 125.0]
[ 22143375.0, 30, 11, 177147.0, 125.0]
[ 66430125.0, 33, 12, 531441.0, 125.0]
[ 199290375.0, 36, 13, 1594323.0, 125.0]
[ 597871125.0, 39, 14, 4782969.0, 125.0]
[ 1793613375.0, 42, 15, 14348907.0, 125.0]
[ 5380840125.0, 45, 16, 43046721.0, 125.0]
[ 16142520375.0, 48, 17, 129140163.0, 125.0]
[ 48427561125.0, 51, 18, 387420489.0, 125.0]
[ 145282683375.0, 54, 19, 1162261467.0, 125.0]
[ 435848050125.0, 57, 20, 3486784401.0, 125.0]
[ 1307544150375.0, 60, 21, 10460353203.0, 125.0]
[ 3922632451125.0, 63, 22, 31381059609.0, 125.0]
[ 11767897353375.0, 66, 23, 94143178827.0, 125.0]

  Posted by Charlie on 2021-03-18 12:41:55
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information