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%I #8 Nov 07 2016 08:54:53
%S 0,40,16,52,160,9232,18952,4372,13120,39364,118096,2480056,5314408,
%T 35075104,9565936,28697812,86093440,1807962280,8523250756,2324522932,
%U 6973568800,20920706404,62762119216,188286357652,564859072960,11862040532200,25418658283288,15251194969972,45753584909920,960825283108360
%N a(n) is the last number in the (2n+1)-element alternating sequence of x/2 and (3x+1) iterations starting with A277215(n).
%C 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.
%C Subsequence of a(n) when q=1 is a subsequence of A100774.
%C Conjecture: this sequence is infinite.
%e 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.
%e 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.
%t (* we use function altdata[] from A277215 *)
%t a277874[n_]:=Map[#[[4]]&, altdata[2,n]]
%t Join[{0,40}, a277874[29]] (*sequence data*)
%Y Cf. A100774, A277215.
%K nonn
%O 0,2
%A _Hartmut F. W. Hoft_, Nov 03 2016
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