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

1,2

Comments

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

Links

Table of n, a(n) for n=1..67.

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

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)

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 *)

Prog

(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

Crossrefs

Cf. A232713.

Sequence in context: A064802 A233570 A181766 * A229089 A277573 A328585

Adjacent sequences: A047581 A047582 A047583 * A047585 A047586 A047587

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved