A353957 a(n) = (85*4^n - 1)/3.

113, 453, 1813, 7253, 29013, 116053, 464213, 1856853, 7427413, 29709653, 118838613, 475354453, 1901417813, 7605671253, 30422685013, 121690740053, 486762960213, 1947051840853, 7788207363413, 31152829453653, 124611317814613, 498445271258453, 1993781085033813

Offset

1,1

Comments

When any term in the sequence is iterated using the Collatz function, its trajectory's only odd number before reaching 1 will be 85.

Also, each term would have 2n+10 steps as its stopping time (A006577).

Links

Table of n, a(n) for n=1..23.

Index entries for linear recurrences with constant coefficients, signature (5,-4).

Formula

From Elmo R. Oliveira, Apr 28 2026: (Start)

a(n) = 5*a(n-1) - 4*a(n-2).

G.f.: x*(113 - 112*x)/((1 - x)*(1 - 4*x)).

E.g.f.: -28 + exp(x)*(-1 + 85*exp(3*x))/3. (End)

Example

When n=5, a(5) = 29013 and when iterated using the Collatz function will have the following trajectory: 87040,43520,21760,10880,5440,2720,1360,680,340,170,85,256,128,64,32,16,8,4,2,1.

Mathematica

(85*4^Range[25] - 1)/3 (* Wesley Ivan Hurt, Nov 10 2023 *)

Prog

(PARI) a(n) = 85*4^n\3 \\ Charles R Greathouse IV, Sep 09 2022

Crossrefs

Subsequence of A198584.

Cf. A006577.

Sequence in context: A111013 A300537 A342816 * A142850 A203722 A118506

Adjacent sequences: A353954 A353955 A353956 * A353958 A353959 A353960

Keyword

nonn,easy

Author

Krishna Kumar Arumugam, Sep 03 2022

Extensions

Simpler definition and more terms from Jon E. Schoenfield, Sep 09 2022

Status

approved