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Search: id:A067433
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| A067433 |
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Triangle in which row n gives trajectory of n under the map k -> k/3 if k is divisible by 3, otherwise k -> next multiple of 3, stopping when reaching 1 (the initial term n is not included). |
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+0
2
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| 1, 3, 1, 1, 6, 2, 3, 1, 6, 2, 3, 1, 2, 3, 1, 9, 3, 1, 9, 3, 1, 3, 1, 12, 4, 6, 2, 3, 1, 12, 4, 6, 2, 3, 1, 4, 6, 2, 3, 1, 15, 5, 6, 2, 3, 1, 15, 5, 6, 2, 3, 1, 5, 6, 2, 3, 1, 18, 6, 2, 3, 1, 18, 6, 2, 3, 1, 6, 2, 3, 1, 21, 7, 9, 3, 1, 2, 1, 7, 9, 3, 1, 7, 9, 3, 1, 24, 8, 9, 3, 1, 24, 8, 9, 3, 1, 8, 9, 3, 1
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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These numbers converge to various last 3 digit endings and only to 2 last 2 digit numbers: 2,1 or 3,1. m=3. p=1 below. If m=2,p=1 you get the x+1 conjecture. If m=2,p=3 you get the 3x+1 conjecture. See Link for large number digit numbers. Other conjectures are possible by trial and error input of m and n. It is interesting to note that for many m and p=m+1 the program converges to 1. However, for m prime and p=m+1 the program always converges to m^2,m,1. Also for m+1 prime the program converges to m^2,m,1 most of the time. An exception is m=6. The sequence converges but to what I call an uninteresting ending.
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LINKS
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Cino Hilliard, The x+1 conjecture
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EXAMPLE
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4 -> 6 -> 2 -> 3 -> 1, so row 4 is 6,2,3,1. Row 5 is the same.
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PROGRAM
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(PARI) multxp2(n, m, p) = { print1(1" "); for(j=1, n, x=j; c=0; while(x>1, r = x%m; if(r==0, x=x/m, x=x*p+m-r); print1(x" "); ); ) }
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CROSSREFS
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Cf. A080816.
Sequence in context: A109446 A088441 A061857 this_sequence A133567 A125230 A162430
Adjacent sequences: A067430 A067431 A067432 this_sequence A067434 A067435 A067436
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KEYWORD
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easy,tabf,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Mar 29 2003
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