

A064433


Number of iterations of A064455 to reach 2 (or 1 in the case of 1).


8



1, 1, 2, 6, 3, 5, 7, 12, 4, 14, 6, 11, 8, 8, 13, 13, 5, 10, 15, 15, 7, 7, 12, 12, 9, 17, 9, 71, 14, 14, 14, 68, 6, 19, 11, 11, 16, 16, 16, 24, 8, 70, 8, 21, 13, 13, 13, 67, 10, 18, 18, 18, 10, 10, 72, 72, 15, 23, 15, 23, 15, 15, 69, 69, 7, 20, 20, 20, 12, 12, 12, 66, 17, 74, 17
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OFFSET

1,3


COMMENTS

Similar to 3x+1 series (A008908). Does this sequence converge to 2 for all values of n (true for all values of n up to 100000)? The inverse sequence using next n = nint(n/2) for n even and n+int(n/2) for n odd leads to 3 (?) possible end sequences (1), (5, 7, 10) and (17, 25, 37, 55, 82, 41, 61, 91, 136, 68, 34)
Starting with a number n, the next value generated is n+int(n/2) if n is even, nint(n/2) if n is odd; a(n) is the number of iteration for the initial value n to reach the limit of 1 to 2
Appears to have the opposite parity to A006666.  Ralf Stephan, Sep 01 2004
Collatz' 3N+1 function as isometry over the dyadics is N>N/2 if even, but N>(3N+1)/2 if odd, including the (necessary) halving into each tripling step. Counting steps until reaching 1 in this way leads to sequence A064433 instead of A008908.  Michael Vielhaber (vielhaber(AT)gmail.com), Nov 18 2009
The value at each step of a trajectory starting with n (n>1) is equal to the value plus one at the same step of the row starting with (n1) of the irregular triangle of the abbreviated (Terrasmodified) Collatz sequence (A070168).  K. Spage, Aug 07 2014


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..19683
M. del P. Canales Chacon, M. J. Vielhaber, Structural and Computational Complexity of Isometries and Their Shift Commutators, Electr. Colloq. on Computational Cpx., ECCC TR04057, 2004. [From Michael Vielhaber (vielhaber(AT)gmail.com), Nov 18 2009]


FORMULA

a(n) = A006666(n1) + 1.  K. Spage, Aug 04 2014


EXAMPLE

a(4) = 6  Starting with 4, 4 is even so the next number is 4+int(4/2) = 6, 6 is even so next number is 6+int(6/2) = 9, 9 is odd so next number is 9int(9/2) = 5, 5 is odd so next number is 5int(5/2) = 3, 3 is odd so next number is 3int(3/2)=2, so giving a sequence of 4,6,9,5,3,2  6 numbers.
a(5) = 3  Starting with 5, A064455(5) = 3, A064455(3) = 2, so giving a trajectory of 5,3,2  3 numbers.  K. Spage, Aug 07 2014


MATHEMATICA

Table[Length@ NestWhileList[If[EvenQ@ #, 3 #/2, (# + 1)/2] &, n, # != 1 + Boole[n > 1] &], {n, 75}] (* Michael De Vlieger, Sep 24 2016 *)


PROG

(PARI) A064455(n) = {if(n%2, (n + 1)/2, 3*n/2)}
A064433(n) = {my(c=1); if(n==1, 1, while(n!=2, n=A064455(n); c++); c)} \\ K. Spage, Aug 07 2014


CROSSREFS

Cf. A008908.
Sequence in context: A259018 A084355 A093650 * A163338 A323335 A139384
Adjacent sequences: A064430 A064431 A064432 * A064434 A064435 A064436


KEYWORD

nonn,easy,look


AUTHOR

Jonathan Ayres (Jonathan.ayres(AT)btinternet.com), Oct 01 2001


STATUS

approved



