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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 15 10:15 EDT 2019. Contains 328026 sequences. (Running on oeis4.)