A047568 Numbers that are congruent to {1, 4, 5, 6, 7} mod 8.

1, 4, 5, 6, 7, 9, 12, 13, 14, 15, 17, 20, 21, 22, 23, 25, 28, 29, 30, 31, 33, 36, 37, 38, 39, 41, 44, 45, 46, 47, 49, 52, 53, 54, 55, 57, 60, 61, 62, 63, 65, 68, 69, 70, 71, 73, 76, 77, 78, 79, 81, 84, 85, 86, 87, 89, 92, 93, 94, 95, 97, 100, 101, 102, 103

Offset

1,2

Links

Table of n, a(n) for n=1..65.

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

Formula

From Chai Wah Wu, Jun 10 2016: (Start)

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

G.f.: x*(x^5 + x^4 + x^3 + x^2 + 3*x + 1)/(x^6 - x^5 - x + 1). (End)

From Wesley Ivan Hurt, Jul 27 2016: (Start)

a(n) = a(n-5) + 8 for n>5.

a(n) = (40*n - 5 + 3*(n mod 5) + 3*((n+1) mod 5) + 3*((n+2) mod 5) - 7*((n+3) mod 5) - 2*((n+4) mod 5))/25.

a(5k) = 8k-1, a(5k-1) = 8k-2, a(5k-2) = 8k-3, a(5k-3) = 8k-4, a(5k-4) = 8k-7. (End)

Maple

A047568:=n->8*floor(n/5)+[1, 4, 5, 6, 7][(n mod 5)+1]: seq(A047568(n), n=0..100); # Wesley Ivan Hurt, Jul 27 2016

Mathematica

Select[Range[100], MemberQ[{1, 4, 5, 6, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Nov 17 2013 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [1, 4, 5, 6, 7]]; // Wesley Ivan Hurt, Jul 27 2016

Crossrefs

Sequence in context: A010399 A215046 A008523 * A139453 A010391 A010419

Adjacent sequences: A047565 A047566 A047567 * A047569 A047570 A047571

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved