

A195906


A periodic sequence.


1



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
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OFFSET

1,1


COMMENTS

Start with a number. If the number is a singledigit 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 5term 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; c.f. 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)/(1x^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



