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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 (list; graph; refs; listen; history; text; internal format)
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 = n-int(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, n-int(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 (n-1) of the irregular triangle of the abbreviated (Terras-modified) 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 TR04-057, 2004. [From Michael Vielhaber (vielhaber(AT)gmail.com), Nov 18 2009]

FORMULA

a(n) = A006666(n-1) + 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 9-int(9/2) = 5, 5 is odd so next number is 5-int(5/2) = 3, 3 is odd so next number is 3-int(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

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Last modified March 21 04:59 EDT 2019. Contains 321364 sequences. (Running on oeis4.)