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A082404
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Triangle in which n-th row gives trajectory of n under the map x -> x/2 if x is even, x -> x-1 if x is odd, stopping when we reach 1.
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2
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1, 2, 1, 3, 2, 1, 4, 2, 1, 5, 4, 2, 1, 6, 3, 2, 1, 7, 6, 3, 2, 1, 8, 4, 2, 1, 9, 8, 4, 2, 1, 10, 5, 4, 2, 1, 11, 10, 5, 4, 2, 1, 12, 6, 3, 2, 1, 13, 12, 6, 3, 2, 1, 14, 7, 6, 3, 2, 1, 15, 14, 7, 6, 3, 2, 1, 16, 8, 4, 2, 1, 17, 16, 8, 4, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| If you write down 0 when divide by 2, 1 when subtract 1, the trajectory gives the binary expansion of n.
The length of the n-th row of the triangle is A056792(n). - Nathaniel Johnston, Apr 21 2011
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 1..10000
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FORMULA
| T(n, 1) = n, T(n, 2) = A029578(n).
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EXAMPLE
| Triangle begins:
1
2 1
3 2 1
4 2 1
5 4 2 1
6 3 2 1
7 6 3 2 1
8 4 2 1
9 8 4 2 1
...
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MAPLE
| A082404 := proc(n, k) option remember: if(k = 1)then return n:elif(A082404(n, k-1) mod 2 = 0)then return A082404(n, k-1)/2: else return A082404(n, k-1)-1: fi: end:
for n from 1 to 20 do k:=1: while A082404(n, k)>=1 do printf("%d, ", A082404(n, k)); k:=k+1: od:printf("\n"); od: # Nathaniel Johnston, Apr 21 2011
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CROSSREFS
| Cf. A056792, A080825.
Sequence in context: A083368 A112379 A073932 * A120885 A193278 A057058
Adjacent sequences: A082401 A082402 A082403 * A082405 A082406 A082407
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KEYWORD
| easy,nonn,tabf
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Apr 14 2003
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EXTENSIONS
| More terms and changed offset from Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), Apr 21 2011
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