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A350279
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Irregular triangle T(n,k) read by rows in which row n lists the iterates of the Farkas map (A349407) from 2*n - 1 to 1.
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8
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1, 3, 1, 5, 3, 1, 7, 11, 17, 9, 3, 1, 9, 3, 1, 11, 17, 9, 3, 1, 13, 7, 11, 17, 9, 3, 1, 15, 5, 3, 1, 17, 9, 3, 1, 19, 29, 15, 5, 3, 1, 21, 7, 11, 17, 9, 3, 1, 23, 35, 53, 27, 9, 3, 1, 25, 13, 7, 11, 17, 9, 3, 1, 27, 9, 3, 1, 29, 15, 5, 3, 1
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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H. M. Farkas, "Variants of the 3N+1 Conjecture and Multiplicative Semigroups", in Entov, Pinchover and Sageev, Geometry, Spectral Theory, Groups, and Dynamics, Contemporary Mathematics, vol. 387, American Mathematical Society, 2005, p. 121.
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FORMULA
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T(n,1) = 2*n-1; T(n,k) = A349407((T(n,k-1)+1)/2), where n >= 1 and k >= 2.
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EXAMPLE
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Written as an irregular triangle, the sequence begins:
n\k 1 2 3 4 5 6 7
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1: 1
2: 3 1
3: 5 3 1
4: 7 11 17 9 3 1
5: 9 3 1
6: 11 17 9 3 1
7: 13 7 11 17 9 3 1
8: 15 5 3 1
9: 17 9 3 1
10: 19 29 15 5 3 1
11: 21 7 11 17 9 3 1
12: 23 35 53 27 9 3 1
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MATHEMATICA
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FarkasStep[x_] := Which[Divisible[x, 3], x/3, Mod[x, 4] == 3, (3*x + 1)/2, True, (x + 1)/2];
Array[Most[FixedPointList[FarkasStep, 2*# - 1]] &, 15] (* Paolo Xausa, Sep 03 2024 *)
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CROSSREFS
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KEYWORD
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nonn,easy,tabf,changed
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AUTHOR
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STATUS
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approved
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