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A047290 Numbers that are congruent to {1, 4, 6} mod 7. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Melvyn B. Nathanson, On the fractional parts of roots of positive real numbers, Amer. Math. Monthly, 120 (2013), 409-429 [see p. 417].
FORMULA
From Colin Barker, Mar 13 2012
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)
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 *)
PROG
(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
CROSSREFS
Sequence in context: A152019 A091181 A189462 * A225002 A086377 A003662
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 29 06:34 EDT 2024. Contains 371265 sequences. (Running on oeis4.)