login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A213243 Number of nonzero elements in GF(2^n) that are cubes. 10
1, 1, 7, 5, 31, 21, 127, 85, 511, 341, 2047, 1365, 8191, 5461, 32767, 21845, 131071, 87381, 524287, 349525, 2097151, 1398101, 8388607, 5592405, 33554431, 22369621, 134217727, 89478485, 536870911, 357913941, 2147483647, 1431655765, 8589934591, 5726623061, 34359738367, 22906492245 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,5,0,-4).

FORMULA

a(n) = M / gcd( M, 3 ), where M=2^n-1.

Conjectures from Colin Barker, Aug 23 2014, verified by Robert Israel, Apr 22 2016: (Start)

a(n) = (-1)*((-2+(-1)^n)*(-1+2^n))/3.

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

G.f.: x*(2*x^2+x+1) / ((x-1)*(x+1)*(2*x-1)*(2*x+1)). (End)

E.g.f.: (-1 + exp(x) - 2*exp(3*x) + 2*exp(4*x))*exp(-2*x)/3. - Ilya Gutkovskiy, Apr 22 2016

MAPLE

A213243:=n->(2^n-1)/gcd(2^n-1, 3): seq(A213243(n), n=1..50); # Wesley Ivan Hurt, Aug 23 2014

MATHEMATICA

Table[(2^n - 1)/GCD[2^n - 1, 3], {n, 50}] (* Vincenzo Librandi, Mar 16 2013 *)

LinearRecurrence[{0, 5, 0, -4}, {1, 1, 7, 5}, 40] (* Harvey P. Dale, Jan 05 2017 *)

PROG

(MAGMA) [(2^n - 1) / GCD (2^n - 1, 3): n in [1..40]]; // Vincenzo Librandi, Mar 16 2013

(PARI) a(n)=(2^n-1)/gcd(2^n-1, 3) \\ Edward Jiang, Sep 04 2014

CROSSREFS

Cf. A213244 (5th powers), A213245 (7th powers), A213246 (9th powers), A213247 (11th powers), A213248 (13th powers).

Sequence in context: A146619 A059990 A213246 * A185269 A070426 A142883

Adjacent sequences:  A213240 A213241 A213242 * A213244 A213245 A213246

KEYWORD

nonn

AUTHOR

Joerg Arndt, Jun 07 2012

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified November 18 17:56 EST 2017. Contains 294894 sequences.