A047369 Numbers that are congruent to {1, 2, 3, 4, 5} mod 7.

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

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 A378844

Adjacent sequences: A047366 A047367 A047368 * A047370 A047371 A047372

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved