login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A305880 A base 3/2 reverse sorted Fibonacci sequence that starts with terms 2211 and 2211. The terms are interpreted as numbers written in base 3/2. To get a(n+2), add a(n) and a(n+1), write the result in base 3/2 and sort the digits into decreasing order, omitting all zeros. 2
2211, 2211, 22211, 22211, 222211, 222211, 2222211, 2222211, 22222211, 22222211, 222222211, 222222211, 2222222211, 2222222211, 22222222211, 22222222211, 222222222211, 222222222211, 2222222222211, 2222222222211, 22222222222211, 22222222222211 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(2n-1) and a(2n) consist of n+1 2's followed by 2 1's.

If a reverse sorted Fibonacci sequence starts with any two numbers, then it eventually becomes either cyclic or turns into this sequence.

In base 10, the corresponding sequence is A069638 and is periodic.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,10,-10).

FORMULA

From Colin Barker, Jun 19 2018: (Start)

G.f.: x*(2211 - 2110*x^2) / ((1 - x)*(1 - 10*x^2)).

a(n) = (2^((n+5)/2+3/2) * 5^((n+5)/2+1/2) - 101) / 9 for n even.

a(n) = (2^((n+9)/2) * 5^((n+7)/2) - 101) / 9 for n odd.

a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3) for n>3.

(End)

EXAMPLE

2211 + 2211 equals 210122 when all numbers are interpreted in base 3/2; after sorting and omitting 0's we obtain a(2) = 22211.

(A305753 has more detailed examples which may help explain the calculations here. - N. J. A. Sloane, Jun 22 2018)

CROSSREFS

Cf. A000045, A024629, A069638, A237575, A305753.

Sequence in context: A226562 A300166 A031772 * A031545 A191679 A349098

Adjacent sequences:  A305877 A305878 A305879 * A305881 A305882 A305883

KEYWORD

nonn,base

AUTHOR

Tanya Khovanova and PRIMES STEP Senior group, Jun 13 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 26 20:57 EDT 2022. Contains 357050 sequences. (Running on oeis4.)