A047497 Numbers that are congruent to {1, 2, 4, 5, 7} mod 8.

1, 2, 4, 5, 7, 9, 10, 12, 13, 15, 17, 18, 20, 21, 23, 25, 26, 28, 29, 31, 33, 34, 36, 37, 39, 41, 42, 44, 45, 47, 49, 50, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 68, 69, 71, 73, 74, 76, 77, 79, 81, 82, 84, 85, 87, 89, 90, 92, 93, 95, 97, 98, 100, 101, 103

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Crossrefs

Cf. A047399 (complement).

Programs

Magma

I:=[1,2,4,5,7]; [n le 5 select I[n] else Self(n-5) + 8 : n in [1..70]]; // Vincenzo Librandi, Jun 06 2017

Maple

seq(floor((8*n-3)/5),n=1..56); # Gary Detlefs, Mar 07 2010

Mathematica

Select[Range[120],MemberQ[{1,2,4,5,7},Mod[#,8]]&] (* or *) LinearRecurrence[ {1,0,0,0,1,-1},{1,2,4,5,7,9},100] (* Harvey P. Dale, Jun 05 2017 *)
Table[8 n + {1, 2, 4, 5, 7}, {n, 0, 20}]//Flatten (* Vincenzo Librandi, Jun 06 2017 *)

PARI

for (n=1, 80, print1((8*n-3)\5, ", ")) \\ Michel Marcus, Sep 10 2014

Formula

a(n) = floor((8n-3)/5). [Gary Detlefs, Mar 07 2010]

From R. J. Mathar, Mar 23 2010: (Start)

a(n) = a(n-1) + a(n-5) - a(n-6).

G.f.: x*(1 + x + 2*x^2 + x^3 + 2*x^4 + x^5)/ ((x^4 + x^3 + x^2 + x + 1) * (x-1)^2). (End)