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!)
A047257 Numbers that are congruent to {4, 5} mod 6. 7
4, 5, 10, 11, 16, 17, 22, 23, 28, 29, 34, 35, 40, 41, 46, 47, 52, 53, 58, 59, 64, 65, 70, 71, 76, 77, 82, 83, 88, 89, 94, 95, 100, 101, 106, 107, 112, 113, 118, 119, 124, 125, 130, 131, 136, 137, 142, 143, 148, 149 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently, numbers m such that 2^m - m is divisible by 3. Indeed, for every prime p, there are infinitely many numbers m such that 2^m - m (A000325) is divisible by p, here are numbers m corresponding to p = 3. - Bernard Schott, Dec 10 2021

REFERENCES

Doob Michael - The Canadian Mathematical Olympiad & L'Olympiade Mathématique du Canada 1969-1993 - Canadian Mathematical Society & Société Mathématique du Canada, Problem 4, 1983, page 158, 1993.

LINKS

Table of n, a(n) for n=1..50.

The IMO Compendium, Problem 4, 15th Canadian Mathematical Olympiad 1983.

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

Index to sequences related to Olympiads.

FORMULA

a(n) = 4 + 6*floor(n/2) + n mod 2.

a(n) = 6*n-a(n-1)-3, with a(1)=4. - Vincenzo Librandi, Aug 05 2010

G.f.: ( x*(4+x+x^2) ) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

a(n) = 3*n-(-1)^n. - Wesley Ivan Hurt, Mar 20 2015

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(6*sqrt(3)) - log(2)/3. - Amiram Eldar, Dec 14 2021

MATHEMATICA

Select[Range@ 150, 4 <= Mod[#, 6] <= 5 &] (* Michael De Vlieger, Mar 20 2015 *)

LinearRecurrence[{1, 1, -1}, {4, 5, 10}, 50] (* Harvey P. Dale, Oct 16 2017 *)

PROG

(Maxima) A047257(n):=4 + 6*floor(n/2) + mod(n, 2)$ akelist(A047257(n), n, 0, 40); /* Martin Ettl, Oct 24 2012 */

CROSSREFS

Cf. A000325.

Similar with: A299174 (p = 2), this sequence (p = 3), A349767 (p = 5).

Sequence in context: A037353 A269003 A246390 * A327311 A151735 A050039

Adjacent sequences:  A047254 A047255 A047256 * A047258 A047259 A047260

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

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 August 18 19:27 EDT 2022. Contains 356215 sequences. (Running on oeis4.)