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!)
A042968 Not divisible by 4. 43
1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 98, 99, 101, 102 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A064680(A064680(a(n))) = a(n). - Reinhard Zumkeller, Oct 19 2001

More generally the sequence of numbers not divisible by some fixed integer m>=2 is given by a(n,m)=n-1+floor((n+m-2)/(m-1)). - Benoit Cloitre, Jul 11 2009

Also a(n,m)=floor((m*n-1)/(m-1)). - Gary Detlefs, May 14 2011

Numbers having not more even than odd divisors: A048272(a(n)) >= 0. - Reinhard Zumkeller, Jan 21 2012

A214546(a(n)) >= 0 for n > 0. - Reinhard Zumkeller, Jul 20 2012

LINKS

Table of n, a(n) for n=0..76.

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

FORMULA

a(n) = +1*a(n-1) +1*a(n-3) -1*a(n-4).

a(n) = 4 + a(n-3).

G.f.: A(x) = (1+x)*(1+x^2) / ( (1+x+x^2)*(x-1)^2 ). - Michael Somos, Jan 12 2000

Nearest integer to sum(k>n, 1/k^4)/sum(k>n, 1/k^5). - Benoit Cloitre, Jun 12 2003

a(n) = n-1+floor((n+2)/3). - Benoit Cloitre, Jul 11 2009

a(n) = floor((4*n-1)/3). - Gary Detlefs, May 14 2011

a(n) = 2*n - ceil(2*n/3) + 1. - Arkadiusz Wesolowski, Sep 21 2012

Sum_{k=0..n} a(n) = A071619(n+1). - L. Edson Jeffery, Jul 30 2014

The g.f. A(x) satisfies x*A(x)^2 = (B(x)/x)^2 + (B(x)/x), where B(x) is the o.g.f. of A042965. - Peter Bala, Apr 12 2017

a(n) = (12*n+6+3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9. - Wesley Ivan Hurt, Sep 30 2017

MATHEMATICA

Select[Table[n, {n, 200}], Mod[#, 4] != 0&] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011 *)

PROG

(PARI) a(n)=1+n+n\3

(PARI) a(n)=n-1+floor((n+2)/3) \\ Benoit Cloitre, Jul 11 2009

(Haskell)

a042968 = (`div` 3) . (subtract 1) . (* 4)

a042968_list = filter ((/= 0) . (`mod` 4)) [1..]

-- Reinhard Zumkeller, Sep 02 2012

(MAGMA) [n-1+Floor((n+2)/3): n in [1..80]]; // Vincenzo Librandi, Aug 03 2015

CROSSREFS

Cf. A001651, A001935, A070048, A042965.

Cf. A071619 (partial sums).

Sequence in context: A039053 A059557 A195291 * A048103 A276078 A193303

Adjacent sequences:  A042965 A042966 A042967 * A042969 A042970 A042971

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 | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 21 17:44 EST 2017. Contains 295004 sequences.