A239129 a(n) = 18*n - 1, n >= 1, the second column of triangle A239127 related to the Collatz problem.

17, 35, 53, 71, 89, 107, 125, 143, 161, 179, 197, 215, 233, 251, 269, 287, 305, 323, 341, 359, 377, 395, 413, 431, 449, 467, 485, 503, 521, 539, 557, 575, 593, 611, 629, 647, 665, 683, 701, 719, 737, 755, 773, 791, 809, 827, 845, 863, 881

Offset

1,1

Comments

This sequence gives all ending values a(n) (in increasing order) of Collatz sequences of length 5 following the pattern (ud)^2, 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. The last entry of this sequence is required to be odd. The first entry is also odd and is given by M(2,n) = 8*n-1 from the array A239126.

This appears as N in Example 2.2. for x=y = 2 in the M. Trümper paper on p. 7, 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

a(n) = 18*n - 1 for n >= 1.

O.g.f.: x*(x+17)/(1-x)^2.

Example

a(1) = 17 because the Collatz sequence for M(2,1) = 8*1 - 1 = 7 from A239126 is [7, 22, 11, 34, 17] ending in the odd number 17.
a(4) = 71 with the Collatz sequence of length 5 starting with M(2,4) = 31 given by [31, 94, 47, 142, 71], ending in a(4).

Mathematica

CoefficientList[Series[(x + 17)/(1 - x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 16 2014 *)

Crossrefs

Cf. A239127, A016969 (first column), A239126.

Sequence in context: A042305 A041566 A004921 * A212427 A195047 A198587

Adjacent sequences: A239126 A239127 A239128 * A239130 A239131 A239132

Keyword

nonn,easy

Author

Wolfdieter Lang, Mar 13 2014

Status

approved