A195906 A periodic sequence.

22, 11, 6, 54, 27, 22, 11, 6, 54, 27, 22, 11, 6, 54, 27, 22, 11, 6, 54, 27, 22, 11, 6, 54, 27, 22, 11, 6, 54, 27, 22, 11, 6, 54, 27, 22, 11, 6, 54, 27, 22, 11, 6, 54, 27, 22, 11, 6, 54, 27, 22, 11, 6, 54, 27, 22, 11, 6, 54, 27, 22, 11, 6, 54, 27, 22, 11, 6

Offset

1,1

Comments

Start with a number. If the number is a single-digit number, multiply it by 9. If the number is a multidigit even number, halve it. If it is a multidigit odd number, subtract 5. Continuing this process leads to a repeating cycle of 5 terms.

There are two different 5-term cycles: 5,45,40,20,10 and 6,54,27,22,11. First corresponds to a(1)=5, second to a(1) = all other positive digits. - Zak Seidov, Sep 25 2011

Links

Muniru A Asiru, Table of n, a(n) for n = 1..2000

T. Trotter, Beyond Ulam [Cached copy; cf. Terrel Trotter's user page]

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).

Formula

G.f.: x*(22 + 11*x + 6*x^2 + 54*x^3 + 27*x^4)/(1 - x^5). - Chai Wah Wu, Jun 04 2016

Maple

seq(coeff(series(x*(22+11*x+6*x^2+54*x^3+27*x^4)/(1-x^5), x, n+1), x, n), n = 1 .. 80); # Muniru A Asiru, Dec 08 2018

Mathematica

f[n_] := If[n < 10, 9n, If[EvenQ[n], n/2, n - 5]]; NestList[f, 22, 100]  (* Amiram Eldar, Dec 08 2018 *)
LinearRecurrence[{0, 0, 0, 0, 1}, {22, 11, 6, 54, 27}, 80] (* Vincenzo Librandi, Dec 09 2018 *)

Prog

(Magma) &cat [[22, 11, 6, 54, 27]^^20]; // Vincenzo Librandi, Dec 09 2018

Crossrefs

Sequence in context: A196103 A196100 A317870 * A033342 A102612 A040465

Adjacent sequences: A195903 A195904 A195905 * A195907 A195908 A195909

Keyword

nonn,base,easy

Author

Kausthub Gudipati, Sep 25 2011

Status

approved