A032793 Numbers that are congruent to {1, 2, 4} mod 5.

1, 2, 4, 6, 7, 9, 11, 12, 14, 16, 17, 19, 21, 22, 24, 26, 27, 29, 31, 32, 34, 36, 37, 39, 41, 42, 44, 46, 47, 49, 51, 52, 54, 56, 57, 59, 61, 62, 64, 66, 67, 69, 71, 72, 74, 76, 77, 79, 81, 82, 84, 86, 87, 89, 91, 92, 94, 96, 97, 99, 101, 102, 104, 106, 107, 109

Offset

1,2

Links

Guenther Schrack, 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) for n>4.

a(n) = floor((5*n-2)/3). - Gary Detlefs, May 14 2011

G.f.: x*(1+x+2*x^2+x^3)/((1+x+x^2)*(1-x)^2). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jun 14 2016: (Start)

a(n) = (15*n - 9 + 2*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 5k - 1, a(3k-1) = 5k - 3, a(3k-2) = 5k - 4. (End)

E.g.f.: (9 + 3*(5*x - 3)*exp(x) + 2*sqrt(3)*sin(sqrt(3)*x/2)*(cosh(x/2) - sinh(x/2)))/9. - Ilya Gutkovskiy, Jun 14 2016

From Guenther Schrack, Oct 31 2019: (Start)

a(n) = a(n-3) + 5 with a(1) = 1, a(2) = 2, a(3) = 4 for n > 3.

a(n) = (15*n - 9 + (w^(2*n) - w^n)*(1 + 2*w))/9 where w = (-1 + sqrt(-3))/2. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(10-2*sqrt(5))*Pi/10 - log(phi)/sqrt(5) + log(2)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 16 2023

Maple

A032793:=n->(15*n-9+2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A032793(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016

Mathematica

Select[Range[0, 200], MemberQ[{1, 2, 4}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 11 2012 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 2, 4, 6}, 90] (* Harvey P. Dale, May 20 2019 *)

Prog

(Magma)[ n: n in [0..120] | n mod 5 in {1, 2, 4} ]; // Vincenzo Librandi, Dec 29 2010
(PARI) a(n)=n\3*5+[-1, 1, 2][n%3+1] \\ Charles R Greathouse IV, Jan 18 2012
(Sage) [(15*n - 9 + 2*sqrt(3)*sin(2*n*pi/3))/9 for n in (1..100)] # G. C. Greubel, Nov 06 2019
(GAP) a:=[1, 2, 4, 6];; for n in [5..100] do a[n]:=a[n-1]+a[n-3]-a[n-4]; od; a; # G. C. Greubel, Nov 06 2019

Crossrefs

Cf. A001622, A032794, A032795.

Sequence in context: A186151 A184732 A039009 * A195127 A292654 A083088

Adjacent sequences: A032790 A032791 A032792 * A032794 A032795 A032796

Keyword

nonn,easy

Author

Patrick De Geest, May 15 1998

Extensions

Better description from Michael Somos, Jun 08 2000

Status

approved