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A047369
Numbers that are congruent to {1, 2, 3, 4, 5} mod 7.
1
1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 57, 58, 59, 60, 61, 64, 65, 66, 67, 68, 71, 72, 73, 74, 75, 78, 79, 80, 81, 82, 85, 86, 87, 88, 89, 92
OFFSET
1,2
FORMULA
G.f.: x*(1+x+x^2+x^3+x^4+2*x^5) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011
From Wesley Ivan Hurt, Aug 08 2016: (Start)
a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6, a(n) = a(n-5) + 7 for n > 5.
a(n) = n + 2*floor((n-1)/5), a(n) = 7*n/5 - 2*(1 + ((n+4) mod 5))/5.
a(5*k) = 7*k-2, a(5*k-1) = 7*k-3, a(5*k-2) = 7*k-4, a(5*k-3) = 7*k-5, a(5*k-4) = 7*k-6. (End)
MAPLE
A047369:=n->7*floor(n/5)+[(1, 2, 3, 4, 5)][(n mod 5)+1]: seq(A047369(n), n=0..100); # Wesley Ivan Hurt, Aug 08 2016
MATHEMATICA
Select[Range[0, 100], MemberQ[{1, 2, 3, 4, 5}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Aug 08 2016 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {1, 2, 3, 4, 5, 8}, 100] (* Vincenzo Librandi, Aug 08 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 7 in [1..5]]; // Wesley Ivan Hurt, Aug 08 2016
CROSSREFS
Sequence in context: A288666 A180734 A031482 * A004827 A155941 A046892
KEYWORD
nonn,easy
STATUS
approved