A221213 -id:A221213 - cp's OEIS frontend

A070991 Numbers n such that the trajectory of n under the `3x+1' map reaches n - 1.

2, 3, 5, 6, 9, 11, 14, 17, 18, 39, 41, 47, 54, 57, 59, 62, 71, 81, 89, 107, 108, 161, 252, 284, 378, 639, 651, 959, 977, 1368, 1439, 1823, 2159, 2430, 2735, 3239, 4103, 4617, 4859, 6155, 7289, 9233

Offset: 1

Benoit Cloitre and Boris Gourevitch (boris(AT)pi314.net), May 18 2002

From Collatz conjecture, the trajectory of n never reaches n again. Is this sequence finite?

There are no more terms < 10^9. - Donovan Johnson, Sep 22 2013

			Trajectory of 39 is: (118, 59, 178, 89, 268, 134, 67, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1) and 39-1 = 38 is reached, hence 39 is in the sequence.

Cf. A070165 (Collatz trajectories), A219696, A221213, A070993.

a070991 n = a070991_list !! (n-1)
a070991_list = filter (\x -> (x - 1) `elem` a070165_row x) [1..]
-- Reinhard Zumkeller, Feb 22 2013

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Select[Range[100000], MemberQ[Collatz[#], # - 1] &] (* T. D. Noe, Feb 21 2013 *)

for(n=1,10000,s=n; t=0; while(s!=1,t++; if(s%2==0,s=s/2,s=3*s+1); if(s==n-1,print1(n,","); ); ))

A070993 Numbers n such that the trajectory of n under the "3x+1" map reaches n+1.

Original entry on oeis.org

3, 7, 9, 15, 19, 25, 33, 39, 51, 91, 121, 159, 166, 183, 243, 250, 333, 376, 411, 432, 487, 501, 649, 667, 865, 889, 975, 1153, 1185, 1299, 1335, 1731, 1779, 2307, 3643, 4857, 7287

Offset: 1

Benoit Cloitre and Boris Gourevitch (boris(AT)pi314.net), May 18 2002

nonn

From Collatz conjecture, the trajectory of n never reaches n again. Is this sequence finite? (it seems there are no further terms below 10^6).

There are no more terms < 10^9. - Donovan Johnson, Sep 22 2013

			Trajectory of 39 is (118, 59, 178, 89, 268, 134, 67, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1) which contains 39+1=40, so 39 is in the sequence.

Cf. A070165 (Collatz trajectories), A221213, A222293, A070991.

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Select[Range[100000], MemberQ[Collatz[#], # + 1] &] (* T. D. Noe, Feb 22 2013 *)

for(n=1,10000,s=n; t=0; while(s!=1,t++; if(s%2==0,s=s/2,s=3*s+1); if(s==n-1,print1(n,","); ); ))

Corrected by T. D. Noe, Oct 25 2006

A222293 Conjectured total number of times that k+n appears in the Collatz (3x+1) sequence of k for k = 1, 2, 3,...

Original entry on oeis.org

37, 30, 34, 30, 31, 29, 28, 38, 42, 32, 40, 40, 49, 30, 40, 40, 54, 45, 46, 40, 49, 44, 41, 48, 47, 54, 48, 41, 50, 44, 54, 45, 49, 60, 53, 47, 54, 50, 56, 44, 48, 50, 54, 47, 54, 38, 56, 47, 60, 48, 63, 48, 47, 45, 56, 53, 49, 49, 62, 52, 50, 54, 53, 52, 49, 46

Offset: 1

T. D. Noe, Feb 22 2013

nonn

			a(1) = 37 because k+1 occurs in the Collatz sequence of k for the 37 values in A070993.

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A070993, A221213 (k-n).

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 75; t = Table[0, {nn}]; lastChange = 10; k = 0; While[k < 2*lastChange, k++; c = Collatz[k]; d = Intersection[Range[nn], c - k]; If[Length[d] > 0, lastChange = k; t[[d]]++]]

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A070991 Numbers n such that the trajectory of n under the `3x+1' map reaches n - 1.

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A070993 Numbers n such that the trajectory of n under the "3x+1" map reaches n+1.

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A222293 Conjectured total number of times that k+n appears in the Collatz (3x+1) sequence of k for k = 1, 2, 3,...

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