A239124 a(n) = 64*n - 11 for n >= 1. Third column of triangle A238476.

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Adjacent sequences: A239121 A239122 A239123 * A239125 A239126 A239127

Keyword

nonn,easy

Author

Wolfdieter Lang, Mar 10 2014

Status

approved