

A075677


Reduced Collatz function R applied to the odd integers: a(n) = R(2n1), where R(k) = (3k+1)/2^r, with r as large as possible.


9



1, 5, 1, 11, 7, 17, 5, 23, 13, 29, 1, 35, 19, 41, 11, 47, 25, 53, 7, 59, 31, 65, 17, 71, 37, 77, 5, 83, 43, 89, 23, 95, 49, 101, 13, 107, 55, 113, 29, 119, 61, 125, 1, 131, 67, 137, 35, 143, 73, 149, 19, 155, 79, 161, 41, 167, 85, 173, 11, 179, 91, 185, 47, 191, 97, 197
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OFFSET

1,2


COMMENTS

The even terms a(2i2) = 6i+5 = A016969(i). The odd terms are the same as A065677. Note that this sequence is A016789 with all factors of 2 removed from each term. Also note that a(4i1) = a(i). No multiple of 3 is in this sequence. See A075680 for the number of iterations of R required to yield 1.


REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, E16.
J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010; see p. 57, also (909), p. 306.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 323.
Eric Weisstein's World of Mathematics, Collatz Problem
Index entries for sequences related to 3x+1 (or Collatz) problem


FORMULA

a(n) = A000265(6*n2).  Reinhard Zumkeller, Jan 08 2014


EXAMPLE

a(11) = 1 because 21 is the 11th odd number and R(21) = 64/64 = 1.


MAPLE

f:=proc(n) local t1;
if n=1 then RETURN(1) else
t1:=3*n+1;
while t1 mod 2 = 0 do t1:=t1/2; od;
RETURN(t1); fi;
end;
(from N. J. A. Sloane, Jan 21 2011)


MATHEMATICA

nextOddK[n_] := Module[{m=3n+1}, While[EvenQ[m], m=m/2]; m]; (* assumes odd n *) Table[nextOddK[n], {n, 1, 200, 2}]


PROG

(PARI) a(n)=n+=2*n1; n>>valuation(n, 2) \\ Charles R Greathouse IV, Jul 05 2013
(Haskell)
a075677 = a000265 . subtract 2 . (* 6)  Reinhard Zumkeller, Jan 08 2014


CROSSREFS

Cf. A016789, A016969, A065677, A075680.
Sequence in context: A131782 A242060 A185953 * A051853 A159074 A147414
Adjacent sequences: A075674 A075675 A075676 * A075678 A075679 A075680


KEYWORD

easy,nonn


AUTHOR

T. D. Noe, Sep 25 2002


STATUS

approved



