A168224 -id:A168224 - cp's OEIS frontend

A047342 Numbers that are congruent to {0, 3, 4} mod 7.

0, 3, 4, 7, 10, 11, 14, 17, 18, 21, 24, 25, 28, 31, 32, 35, 38, 39, 42, 45, 46, 49, 52, 53, 56, 59, 60, 63, 66, 67, 70, 73, 74, 77, 80, 81, 84, 87, 88, 91, 94, 95, 98, 101, 102, 105, 108, 109, 112, 115, 116, 119, 122, 123, 126, 129, 130, 133, 136, 137, 140

Offset: 1

N. J. A. Sloane

Record values in A168223: a(n) = A168223(A168224(n)) and A168223(m) < a(n) for m < A168224(n). - Reinhard Zumkeller, Nov 20 2009

Also: Numbers n such that kronecker(n^2-4,7) = -1. - M. F. Hasler, Mar 14 2013

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

Cf. A168223, A168224.

[n : n in [0..150] | n mod 7 in [0, 3, 4]]; // Wesley Ivan Hurt, Jun 13 2016

A047342:=n->(21*n-21-6*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047342(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016

Select[Range[0,150], MemberQ[{0,3,4}, Mod[#,7]]&] (* Harvey P. Dale, Mar 18 2011 *)
CoefficientList[Series[(3x+x^2+3x^3)/((-1+x)^2(1+x+x^2)),{x,0,160}],x] (* Vladimir Joseph Stephan Orlovsky, Jan 26 2012 *)
LinearRecurrence[{1, 0, 1, -1},{0, 3, 4, 7},61] (* Ray Chandler, Aug 25 2015 *)

G.f.: x(3+x+3x^2)/((1-x)^2*(1+x+x^2)). - R. J. Mathar, Sep 17 2008
a(n) = a(n-1) + a(n-3) - a(n-4), n>4. - Vincenzo Librandi, Mar 24 2011
From Wesley Ivan Hurt, Jun 13 2016: (Start)
a(n) = (21*n-21-6*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 7k-3, a(3k-1) = 7k-4, a(3k-2) = 7k-7. (End)

A168223 a(n) = A006369(n) - A006368(n).

Original entry on oeis.org

0, 0, 0, 0, -1, 3, -5, 4, -1, -1, -2, 7, -10, 7, -2, -1, -3, 10, -15, 11, -3, -2, -4, 14, -20, 14, -4, -2, -5, 17, -25, 18, -5, -3, -6, 21, -30, 21, -6, -3, -7, 24, -35, 25, -7, -4, -8, 28, -40, 28, -8, -4, -9, 31, -45, 32, -9, -5, -10, 35, -50, 35, -10, -5, -11, 38, -55, 39

Offset: 0

Reinhard Zumkeller, Nov 20 2009

A047342 and A168223 give record values and where they occur: a(A168224(n))=A047342(n) and a(m) < A047342(n) for m < A168224(n).

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for sequences related to 3x+1 (or Collatz) problem
Index entries for linear recurrences with constant coefficients, signature (-2,-2,0,3,4,3,0,-2,-2,-1).

a168223 n = a006369 n - a006368 n  -- Reinhard Zumkeller, Mar 15 2014

LinearRecurrence[{-2,-2,0,3,4,3,0,-2,-2,-1},{0, 0, 0, 0, -1, 3, -5, 4, -1, -1},50] (* G. C. Greubel, Jul 16 2016 *)

a(12*n) = -10*n,          a(12*n+1) = 7*n.
a(12*n+2) = -2*n,         a(12*n+3) = -n.
a(12*n+4) = -2*n - 1,     a(12*n+5) = 7*n + 3.
a(12*n+6) = -10*n - 5,    a(12*n+7) = 7*n + 4.
a(12*n+8) = -2*n -1,      a(12*n+9) = -n - 1.
a(12*n+10) = -2*n - 2,    a(12*n+11) = 7*n + 7.
G.f.: -x^4*(x^2-x+1) / ((x-1)^2*(x+1)^2*(x^2+1)*(x^2+x+1)^2). - Colin Barker, Apr 04 2013

cp's OEIS Frontend

A047342 Numbers that are congruent to {0, 3, 4} mod 7.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

Formula