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A239124
a(n) = 64*n - 11 for n >= 1. Third column of triangle A238476.
2
53, 117, 181, 245, 309, 373, 437, 501, 565, 629, 693, 757, 821, 885, 949, 1013, 1077, 1141, 1205, 1269, 1333, 1397, 1461, 1525, 1589, 1653, 1717, 1781, 1845, 1909, 1973, 2037, 2101, 2165, 2229, 2293, 2357, 2421
OFFSET
1,1
COMMENTS
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.
This appears in Example 2.1. for x = 5 in the M. Trümper paper given as a link below.
LINKS
Wolfdieter Lang, On Collatz' Words, Sequences, and Trees, J. of Integer Sequences, Vol. 17 (2014), Article 14.11.7.
Manfred Trümper, The Collatz Problem in the Light of an Infinite Free Semigroup, Chinese Journal of Mathematics, Vol. 2014, Article ID 756917, 21 pages.
FORMULA
O.g.f.: x*(53+11*x)/(1-x)^2.
EXAMPLE
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.
MATHEMATICA
CoefficientList[Series[(53 + 11 x)/(1 - x)^2, {x, 0, 50}], x] (* Vincenzo Librandi, Mar 13 2014 *)
64 Range[40]-11 (* Harvey P. Dale, Nov 21 2018 *)
PROG
(Magma) [64*n-11: n in [1..50]]; // Vincenzo Librandi, Mar 13 2014
CROSSREFS
Cf. A238476, A004767 (first column), A082285 (second column).
Sequence in context: A104073 A044240 A044621 * A254210 A142125 A177105
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Mar 10 2014
STATUS
approved