A238477 a(n) = 32*n - 27 for n >= 1. Second column of triangle A238475.

5, 37, 69, 101, 133, 165, 197, 229, 261, 293, 325, 357, 389, 421, 453, 485, 517, 549, 581, 613, 645, 677, 709, 741, 773, 805, 837, 869, 901, 933, 965, 997, 1029, 1061, 1093, 1125, 1157, 1189, 1221, 1253, 1285, 1317, 1349, 1381, 1413, 1445

Offset

1,1

Comments

This sequence gives all start numbers a(n) (sorted increasingly) of Collatz sequences of length 6 following the pattern udddd = ud^4, 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 and it is given by 6*n - 5.

This appears in Example 2.1. for x = 4 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*(5+27*x)/(1-x)^2.

Example

a(1) = 5 because the Collatz sequence of length 6 is [5, 16, 8, 4, 2, 1], following the pattern udddd, ending in 1, and 5 is the smallest start number following this pattern ending in an odd number.
a(2) = 37 with the length 6 Collatz sequence [37, 112, 56, 28, 14, 7] ending in 12 - 5 = 7, and this is the second smallest start number with this sequence pattern ending in an odd number.

Mathematica

CoefficientList[Series[(5 + 27 x)/(1 - x)^2, {x, 0, 50}], x] (* Vincenzo Librandi, Mar 12 2014 *)

Crossrefs

Cf. A238475, A017077 (first column), A239123 (third column).

Sequence in context: A141182 A127589 A244374 * A213049 A031913 A188130

Adjacent sequences: A238474 A238475 A238476 * A238478 A238479 A238480

Keyword

nonn,easy

Author

Wolfdieter Lang, Mar 10 2014

Status

approved