A047488 Numbers that are congruent to {0, 2, 3, 5, 7} mod 8.

0, 2, 3, 5, 7, 8, 10, 11, 13, 15, 16, 18, 19, 21, 23, 24, 26, 27, 29, 31, 32, 34, 35, 37, 39, 40, 42, 43, 45, 47, 48, 50, 51, 53, 55, 56, 58, 59, 61, 63, 64, 66, 67, 69, 71, 72, 74, 75, 77, 79, 80, 82, 83, 85, 87, 88, 90, 91, 93, 95, 96, 98, 99, 101, 103

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Different from A022342.

Programs

Magma

[n : n in [0..150] | n mod 8 in [0, 2, 3, 5, 7]]; // Wesley Ivan Hurt, Jul 31 2016

Maple

A047488:=n->8*floor(n/5)+[(0, 2, 3, 5, 7)][(n mod 5)+1]: seq(A047488(n), n=0..100); # Wesley Ivan Hurt, Jul 31 2016

Mathematica

Select[Range[0,150], MemberQ[{0, 2, 3, 5, 7}, Mod[#,8]]&] (* Harvey P. Dale, Mar 20 2011 *)

Formula

G.f.: x^2*(2+x+2*x^2+2*x^3+x^4)/((1-x)^2*(1+x+x^2+x^3+x^4)). [Colin Barker, May 14 2012]

From Wesley Ivan Hurt, Jul 31 2016: (Start)

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6, a(n) = a(n-5) + 8 for n > 5.

a(n) = (40*n - 35 - 2*(n mod 5) - 2*((n+1) mod 5) + 3*((n+2) mod 5) - 2*((n+3) mod 5) + 3*((n+4) mod 5))/25.

a(5k) = 8k-1, a(5k-1) = 8k-3, a(5k-2) = 8k-5, a(5k-3) = 8k-6, a(5k-4) = 8k-8. (End)