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A220182 Number of changes of parity in the Collatz trajectory of n. 1
0, 1, 4, 1, 2, 5, 10, 1, 12, 3, 8, 5, 4, 11, 10, 1, 6, 13, 12, 3, 2, 9, 8, 5, 14, 5, 82, 11, 10, 11, 78, 1, 16, 7, 6, 13, 12, 13, 22, 3, 80, 3, 18, 9, 8, 9, 76, 5, 14, 15, 14, 5, 4, 83, 82, 11, 20, 11, 20, 11, 10, 79, 78, 1, 16, 17, 16, 7, 6, 7, 74, 13, 84, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

For n < 10^10, if n <> 27, f(n) is finite, f(n) < 3n + 1. If n = 27 = 3^3, f(n) = 82 = 81 + 1 = 3^4 + 1 = 3n + 1. I conjecture that for any n <> 27, f(n) is finite, f(n) < 3n + 1. - Sergey Pavlov, Jun 02 2019. Note that this conjecture is stronger than the Collatz conjecture. - Andrey Zabolotskiy,  Jun 13 2019

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, E16

LINKS

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

EXAMPLE

For n=5, Collatz trajectory for 5 is: 5,16,8,4,2,1; hence no. of transitions between odd and even parity is a(5)=2; similarly for n=11, Collatz trajectory gives 11,34,17,52,26,13,40,20,10,5,16,8,4,2,1; implies that a(11)=8.

MATHEMATICA

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; parity[n_] := If[OddQ[n], 1, 0]; Table[p = parity /@ Collatz[n]; If[OddQ[n], 2*Total[p] - 2, 2*Total[p] - 1], {n, 100}] (* T. D. Noe, Feb 24 2013 *)

PROG

(PARI) next_iter(n) = if(n%2==0, return(n/2), return(3*n+1))

parity(n) = n%2

a(n) = my(x=n, par=parity(x), i=0); while(x > 1, x=next_iter(x); if(parity(x)!=par, i++; par=parity(x))); i \\ Felix Fröhlich, Jun 02 2019

CROSSREFS

Cf. A006577.

Sequence in context: A046573 A006287 A087225 * A076064 A293570 A016685

Adjacent sequences:  A220179 A220180 A220181 * A220183 A220184 A220185

KEYWORD

nonn,look

AUTHOR

Jayanta Basu, Feb 20 2013

STATUS

approved

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Last modified October 28 13:26 EDT 2020. Contains 338055 sequences. (Running on oeis4.)