[go: up one dir, main page]

login
A047391
Numbers that are congruent to {1, 3, 5} mod 7.
3
1, 3, 5, 8, 10, 12, 15, 17, 19, 22, 24, 26, 29, 31, 33, 36, 38, 40, 43, 45, 47, 50, 52, 54, 57, 59, 61, 64, 66, 68, 71, 73, 75, 78, 80, 82, 85, 87, 89, 92, 94, 96, 99, 101, 103, 106, 108, 110, 113, 115, 117, 120, 122, 124, 127, 129, 131, 134, 136, 138, 141
OFFSET
1,2
FORMULA
From Bruno Berselli, Mar 25 2011: (Start)
G.f.: x*(1+2*x+2*x^2+2*x^3)/((1-x)^2*(1+x+x^2)).
a(n) = 7*floor((n-1)/3)+2*(n-1 mod 3)+1.
a(n) = (1/3)*(7*n-5-A049347(n)). (End)
From Wesley Ivan Hurt, Jun 13 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = (21*n-15-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*Pi*n/3))/9.
a(3k) = 7k-2, a(3k-1) = 7k-4, a(3k-2) = 7k-6. (End)
a(n) = n - 1 + floor((4n-1)/3). - Wesley Ivan Hurt, Dec 27 2016
MAPLE
A047391:=n->(21*n-15-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*Pi*n/3))/9: seq(A047391(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016
MATHEMATICA
Select[Range[0, 150], MemberQ[{1, 3, 5}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 13 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 3, 5, 8}, 100] (* Vincenzo Librandi, Jun 14 2016 *)
PROG
(Magma) [n: n in [1..122] | n mod 7 in [1, 3, 5]]; // Bruno Berselli, Mar 25 2011
CROSSREFS
Cf. A049347.
Sequence in context: A342871 A191160 A189929 * A184655 A090846 A195170
KEYWORD
nonn,easy
STATUS
approved