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).

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

Offset: 0

Author

Hartmut F. W. Hoft, Nov 03 2016

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A100774, A277215.

Programs

Mathematica

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