

A277874


a(n) is the last number in the (2n+1)element alternating sequence of x/2 and (3x+1) iterations starting with A277215(n).


2



0, 40, 16, 52, 160, 9232, 18952, 4372, 13120, 39364, 118096, 2480056, 5314408, 35075104, 9565936, 28697812, 86093440, 1807962280, 8523250756, 2324522932, 6973568800, 20920706404, 62762119216, 188286357652, 564859072960, 11862040532200, 25418658283288, 15251194969972, 45753584909920, 960825283108360
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OFFSET

0,2


COMMENTS

a(n) has the form 2*(q*3^n  1) where q is the smallest odd number so that the alternating Collatz sequence of 2n+1 elements starting at 2*(q*2^n  1) ends at the maximum of its Collatz trajectory.
Subsequence of a(n) when q=1 is a subsequence of A100774.
Conjecture: this sequence is infinite.


LINKS

Table of n, a(n) for n=0..29.


EXAMPLE

a(0) = 0 = 2*(1*3^0  1) since it is the start and end of the first alternating sequence of 1 element and the maximum of its trajectory.
a(5) = 9232 = 2*(19*3^5  1) is the last element in the first alternating sequence of 11 elements [1214, 607, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232] that ends in the trajectory maximum.


MATHEMATICA

(* we use function altdata[] from A277215 *)
a277874[n_]:=Map[#[[4]]&, altdata[2, n]]
Join[{0, 40}, a277874[29]] (*sequence data*)


CROSSREFS

Cf. A100774, A277215.
Sequence in context: A181643 A117831 A152143 * A033975 A033360 A029543
Adjacent sequences: A277871 A277872 A277873 * A277875 A277876 A277877


KEYWORD

nonn


AUTHOR

Hartmut F. W. Hoft, Nov 03 2016


STATUS

approved



