The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A042968 Numbers not divisible by 4. 55
 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 1,2 COMMENTS Equivalently, numbers whose square part is odd. Cf. A028982. - Peter Munn, Jul 14 2020 More generally the sequence of numbers not divisible by some fixed integer m >= 2 is given by a(n,m) = 1 + n + floor(n/(m-1)). - Benoit Cloitre, Jul 11 2009 Also a(n,m) = floor((m*n-1)/(m-1)) [with offset 1]. - Gary Detlefs, May 14 2011 Numbers not having more even than odd divisors: A048272(a(n)) >= 0. - Reinhard Zumkeller, Jan 21 2012 Extending the comments of Benoit Cloitre (Jul 11 2009) and Gary Detlefs (May 14 2011), the g.f. is A(m,x) = (1-x^m) / ((1-x^(m-1))*(1-x)^2) where m >= 2 is fixed. - Werner Schulte, Apr 26 2018 LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1). FORMULA a(n) = a(n-1) + a(n-3) - a(n-4). a(n) = a(n-3) + 4, with a(1) = 1. G.f.: x * (1+x) * (1+x^2) / ( (1+x+x^2)*(1-x)^2 ). - Michael Somos, Jan 12 2000 A064680(A064680(a(n))) = a(n). - Reinhard Zumkeller, Oct 19 2001 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/3). - Benoit Cloitre, Jul 11 2009 a(n) = floor((4*n+3)/3). - Gary Detlefs, May 14 2011 A214546(a(n)) >= 0 for n > 0. - Reinhard Zumkeller, Jul 20 2012 a(n) = 2*n - ceiling(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 Euler transform of length 4 sequence [2, 0, 1, -1]. - Michael Somos, Jun 17 2018 a(n) = -a(-1-n) for all n in Z. - Michael Somos, Jun 17 2018 E.g.f.: (2/3)*exp(x)*(1 + 2*x) + (1/9)*exp(-x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2)). - Stefano Spezia, Nov 16 2019 a(n) = (12*n + 6 + w^(2*n)*(w + 2) - w^n*(w - 1))/9 where w = (-1 + sqrt(-3))/2. - Guenther Schrack, Jun 07 2021 Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)-1)*Pi/8. - Amiram Eldar, Dec 05 2021 EXAMPLE G.f. = 1 + 2*x + 3*x^2 + 5*x^3 + 6*x^4 + 7*x^5 + 9*x^6 + 10*x^7 + 11*x^8 + ... - Michael Somos, Jun 17 2018 MAPLE seq(n+floor((n-1)/3), n=1..80); # Muniru A Asiru, Feb 17 2019 MATHEMATICA Select[Table[n, {n, 200}], Mod[#, 4] != 0&] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011 *) PROG (PARI) {a(n) = 1 + n + n\3}; (Haskell) a042968 = (`div` 3) . (subtract 1) . (* 4) a042968_list = filter ((/= 0) . (`mod` 4)) [1..] -- Reinhard Zumkeller, Sep 02 2012 (MAGMA) [n+1+Floor(n/3): n in [0..80]]; // Vincenzo Librandi, Aug 03 2015 (Sage) [1+n+floor(n/3) for n in (0..80)] # G. C. Greubel, Feb 17 2019 CROSSREFS Cf. A001651, A001935, A028982, A070048, A042965, A064680. Cf. A071619 (partial sums); A008586 (complement). Numbers that are congruent to {k0,k1,k2} mod 4: A004772, A004773, A042965, a(n). Sequence in context: A329974 A059557 A195291 * A337037 A048103 A276078 Adjacent sequences:  A042965 A042966 A042967 * A042969 A042970 A042971 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Dec 11 1999 EXTENSIONS Edited by Peter Munn, Nov 16 2019 I restored my original (1999) definition and offset, which in the intervening 21 years had been lost. - N. J. A. Sloane, Jun 12 2021 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.

Last modified June 29 09:21 EDT 2022. Contains 354910 sequences. (Running on oeis4.)