

A129304


Numbers n such that the Collatz iteration requires a different number of halving and tripling steps than any previous number.


2



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 17, 18, 20, 22, 24, 25, 27, 28, 31, 32, 33, 34, 36, 39, 40, 41, 43, 44, 47, 48, 49, 54, 56, 57, 62, 64, 65, 68, 71, 72, 73, 78, 80, 82, 86, 88, 91, 94, 96, 97, 98, 103, 105, 107, 108, 111, 112, 114, 121, 123, 124, 128, 129, 130
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OFFSET

1,2


COMMENTS

Note that if n is in this sequence, then 2n is also. The plot shows a very narrow triangle of the possible halving/tripling pairs. As n increases, the width of the triangle grows on its right edge.


LINKS

T. D. Noe, Table of n, a(n) for n=1..2000
T. D. Noe, Plot of the 2000 possible halving/tripling pairs for n <= 7540196


EXAMPLE

Each any n, let the ordered pair (h,t) give the number of halving and tripling steps in the Collatz iteration. The pairs for the first 16 numbers are (0,0), (1,0), (5,2), (2,0), (4,1), (6,2), (11,5), (3,0), (13,6), (5,1), (10,4), (7,2), (7,2), (12,5), (12,5), (4,0). Thus 13 and 15 are not in this sequence because their pairs are the same as for 12 and 14, respectively.


MATHEMATICA

Collatz[n_] := Module[{c1=0, c2=0, m=n}, While[m>1, If[EvenQ[m], c1++; m=m/2, c2++; m=3m+1]]; {c1, c2}]; s={}; t={}; n=0; While[Length[t]<100, n++; c=Collatz[n]; If[ !MemberQ[s, c], AppendTo[s, c]; AppendTo[t, n]]]; t


CROSSREFS

Cf. A006666 (number of halving steps), A006667 (number of tripling steps).
Sequence in context: A172974 A066255 A302593 * A294358 A262358 A032962
Adjacent sequences: A129301 A129302 A129303 * A129305 A129306 A129307


KEYWORD

nonn


AUTHOR

T. D. Noe, Apr 09 2007


STATUS

approved



