A047584 Numbers that are congruent to {1, 3, 5, 6, 7} mod 8.

1, 3, 5, 6, 7, 9, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 27, 29, 30, 31, 33, 35, 37, 38, 39, 41, 43, 45, 46, 47, 49, 51, 53, 54, 55, 57, 59, 61, 62, 63, 65, 67, 69, 70, 71, 73, 75, 77, 78, 79, 81, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 99, 101, 102, 103, 105, 107

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Numbers n such that A232713(n) is divisible by n. [Bruno Berselli, Dec 11 2013]

Links

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

Crossrefs

Cf. A232713.

Programs

Mathematica

Select[Range@ 107, Or[OddQ@ Mod[#, 8], Mod[#, 8] == 6] &] (* Michael De Vlieger, Oct 23 2015 *)
#+{1,3,5,6,7}&/@(8*Range[0,20])//Flatten (* Harvey P. Dale, May 13 2019 *)

PARI

x='x+O('x^100); Vec((1+x)*(1+x+x^2+x^4)/((1-x)^2*(1+x+x^2+x^3+ x^4))) \\ Altug Alkan, Oct 22 2015

Formula

G.f.: (1 + x)*(1 + x + x^2 + x^4) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)). [Bruno Berselli, Dec 11 2013]

From Wesley Ivan Hurt, Dec 30 2016: (Start)

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

a(n) = (40n - 10 + 3*(n mod 5) + 3*((n+1) mod 5) - 2*((n+2) mod 5) - 2*((n+3) mod 5) - 2*((n+4) mod 5))/25. (End)