A047290 Numbers that are congruent to {1, 4, 6} mod 7.

1, 4, 6, 8, 11, 13, 15, 18, 20, 22, 25, 27, 29, 32, 34, 36, 39, 41, 43, 46, 48, 50, 53, 55, 57, 60, 62, 64, 67, 69, 71, 74, 76, 78, 81, 83, 85, 88, 90, 92, 95, 97, 99, 102, 104, 106, 109, 111, 113, 116, 118, 120, 123, 125, 127, 130, 132, 134, 137, 139, 141

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• Melvyn B. Nathanson, On the fractional parts of roots of positive real numbers, Amer. Math. Monthly, 120 (2013), 409-429 [see p. 417].
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Programs

Magma

I:=[1, 4, 6, 8]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi Apr 26 2012

Maple

A047290:=n->(21*n-9-2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047290(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016

Mathematica

Select[Range[0,12000], MemberQ[{1,4,6}, Mod[#,7]]&] (* Vincenzo Librandi, Apr 26 2012 *)
LinearRecurrence[{1,0,1,-1}, {1,4,6,8}, 60] (* Harvey P. Dale, Sep 19 2014 *)

Formula

From Colin Barker, Mar 13 2012: (Start)

G.f.: x*(1+3*x+2*x^2+x^3)/((1-x)^2*(1+x+x^2)).

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. (End)

From Wesley Ivan Hurt, Jun 13 2016: (Start)

a(n) = (21*n-9-2*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 7k-1, a(3k-1) = 7k-3, a(3k-2) = 7k-6. (End)