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%I #23 Sep 08 2022 08:46:07
%S 53,117,181,245,309,373,437,501,565,629,693,757,821,885,949,1013,1077,
%T 1141,1205,1269,1333,1397,1461,1525,1589,1653,1717,1781,1845,1909,
%U 1973,2037,2101,2165,2229,2293,2357,2421
%N a(n) = 64*n - 11 for n >= 1. Third column of triangle A238476.
%C This sequence gives all start numbers a(n) (sorted increasingly) of Collatz sequences of length 7 following the pattern ud^5 with u (for `up'), mapping an odd number m to 3*m+1, and d (for `down'), mapping an even number m to m/2, requiring that the sequence ends in an odd number. The last entry of this Collatz sequence is 6*n - 1.
%C This appears in Example 2.1. for x = 5 in the M. Trümper paper given as a link below.
%H Vincenzo Librandi, <a href="/A239124/b239124.txt">Table of n, a(n) for n = 1..1000</a>
%H Wolfdieter Lang, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Lang/lang6.html">On Collatz' Words, Sequences, and Trees</a>, J. of Integer Sequences, Vol. 17 (2014), Article 14.11.7.
%H Manfred Trümper, <a href="http://dx.doi.org/10.1155/2014/756917">The Collatz Problem in the Light of an Infinite Free Semigroup</a>, Chinese Journal of Mathematics, Vol. 2014, Article ID 756917, 21 pages.
%F O.g.f.: x*(53+11*x)/(1-x)^2.
%e a(1) = 53 because the Collatz sequence of length 7 following the pattern uddddd, ending in an odd number is [53, 160, 80, 40, 20, 10, 5]. The end number is 6*1 - 1 = 5.
%t CoefficientList[Series[(53 + 11 x)/(1 - x)^2, {x, 0, 50}], x] (* _Vincenzo Librandi_, Mar 13 2014 *)
%t 64 Range[40]-11 (* _Harvey P. Dale_, Nov 21 2018 *)
%o (Magma) [64*n-11: n in [1..50]]; // _Vincenzo Librandi_, Mar 13 2014
%Y Cf. A238476, A004767 (first column), A082285 (second column).
%K nonn,easy
%O 1,1
%A _Wolfdieter Lang_, Mar 10 2014
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