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A070165 Irregular triangle read by rows giving trajectory of n in Collatz problem. 80
1, 2, 1, 3, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, 5, 16, 8, 4, 2, 1, 6, 3, 10, 5, 16, 8, 4, 2, 1, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 8, 4, 2, 1, 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 10, 5, 16, 8, 4, 2, 1, 11, 34, 17, 52, 26, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

n-th row has A008908(n) entries (unless some n never reaches 1, in which case the triangle ends with an infinite row). [Escape clause added by N. J. A. Sloane, Jun 06 2017]

A216059(n) is the smallest number not occurring in n-th row; see also A216022.

LINKS

T. D. Noe, Rows n=1..100 of triangle, flattened

David Rabahy, Hailstone Sequence presented as a spreadsheet

Anatoly E. Voevudko, File of first 10K Collatz sequences

Eric Weisstein's World of Mathematics, Collatz Problem

Wikipedia, Collatz conjecture

Index entries for sequences related to 3x+1 (or Collatz) problem

FORMULA

T(n,k) = T^{(k)}(n) with the k-th iterate of the Collatz map T with T(n) = 3*n+1 if n is odd and T(n) = n/2 if n is even, n >= 1. T^{(0)}(n) = n. k = 0, 1, ..., A008908(n) - 1. - Wolfdieter Lang, Mar 20 2014

EXAMPLE

The irregular array a(n,k) starts:

n\k   0   1   2   3   4    5   6    7   8   9  10  11  12  13  14  15  16  17  18  19 ...

1:    1

2:    2   1

3:    3  10   5  16   8    4   2    1

4:    4   2   1

5:    5  16   8   4   2    1

6:    6   3  10   5  16    8   4    2   1

7:    7  22  11  34  17   52  26   13  40  20  10   5  16   8   4   2   1

8:    8   4   2   1

9:    9  28  14   7  22   11  34   17  52  26  13  40  20  10   5  16   8   4   2   1

10:  10   5  16   8   4    2   1

11:  11  34  17  52  26   13  40   20  10   5  16   8   4   2   1

12:  12   6   3  10   5   16   8    4   2   1

13:  13  40  20  10   5   16   8    4   2   1

14:  14   7  22  11  34   17  52   26  13  40  20  10   5  16   8   4   2   1

15:  15  46  23  70  35  106  53  160  80  40  20  10   5  16   8   4   2   1

... Reformatted and extended by Wolfdieter Lang, Mar 20 2014

------------------------------------------------------------------------------------------

MATHEMATICA

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Flatten[Table[Collatz[n], {n, 10}]] (* T. D. Noe, Dec 03 2012 *)

PROG

(Haskell)

a070165 n k = a070165_tabf !! (n-1) !! (k-1)

a070165_tabf = map a070165_row [1..]

a070165_row n = (takeWhile (/= 1) $ iterate a006370 n) ++ [1]

a070165_list = concat a070165_tabf

-- Reinhard Zumkeller, Oct 07 2011

(PARI) Collatz(n, lim=0)={

my(c=n, e=0, L=List(n)); if(lim==0, e=1; lim=n*10^6);

for(i=1, lim, if(c%2==0, c=c/2, c=3*c+1); listput(L, c); if(e&&c==1, break));

return(Vec(L)); } \\Anatoly E. Voevudko, Mar 26 2016

(PARI) Collatzaf(ns, nf, fn="")={

my(V, vn, fng="aCollatz.txt"); if(fn=="", fn=fng);

for(i=ns, nf, V=Collatz(i); vn=#V; write(fn, Str(i, "/", vn, ": ", V)); kill(V)); }

Collatzaf(1, 10000, "a070165.txt"); \\ a070165.txt file with 10000 rows

\\ Anatoly E. Voevudko, Mar 30 2016

(Python)

def a(n):

....if n==1: return [1]

....l=[n, ]

....while True:

........if n%2==0: n/=2

........else: n = 3*n + 1

........if not n in l:

............l+=[n, ]

............if n<2: break

........else: break

....return l

for n in xrange(1, 101): print a(n) # Indranil Ghosh, Apr 14 2017

CROSSREFS

Cf. A006667.

Cf. A006370, A033493 (row sums).

Cf. A220237 (sorted rows), A192719.

Cf. A070168 (Terras modified Collatz map).

Cf. A254312, A257480 (and crossrefs therein).

Cf. A280408 (primes), added by Matthew Campbell, Jan 2 2017

Sequence in context: A229417 A260758 A091858 * A192719 A270996 A203709

Adjacent sequences:  A070162 A070163 A070164 * A070166 A070167 A070168

KEYWORD

nonn,easy,tabf

AUTHOR

Eric W. Weisstein, Apr 23 2002

EXTENSIONS

Name specified and row length A-number corrected by Wolfdieter Lang, Mar 20 2014

STATUS

approved

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Last modified September 23 17:42 EDT 2017. Contains 292362 sequences.