A047207 Numbers that are congruent to {0, 1, 3, 4} mod 5.

0, 1, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 56, 58, 59, 60, 61, 63, 64, 65, 66, 68, 69, 70, 71, 73, 74, 75, 76, 78, 79, 80, 81, 83, 84

Offset

1,3

Comments

Numbers not ending in 2 or 7. - Bruno Berselli, Oct 30 2017

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..8000

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

Formula

a(n) = floor((5*n-3)/4). - Gary Detlefs, Mar 06 2010

G.f.: x^2*(1 + 2*x + x^2 + x^3) / ( (1 + x)*(x^2 + 1)*(x - 1)^2 ). - R. J. Mathar, Oct 08 2011

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(1)=3, b(k)=5*2^(k-2) for k>1. - Philippe Deléham, Oct 17 2011

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

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (10*n-9-i^(2*n)+(1-i)*i^(-n)+(1+i)*i^n)/8, where i=sqrt(-1).

a(2*k) = A047209(k), a(2*k-1) = A047218(k). (End)

E.g.f.: (4 - sin(x) + cos(x) + (5*x - 4)*sinh(x) + 5*(x - 1)*cosh(x))/4. - Ilya Gutkovskiy, May 30 2016

Sum_{n>=2} (-1)^n/a(n) = log(5)/4 + 3*sqrt(5)*log(phi)/10 + sqrt(1-2/sqrt(5))*Pi/10, where phi is the golden ratio (A001622). - Amiram Eldar, Dec 07 2021

Maple

seq(floor((5*n-3)/4), n=1..57); # Gary Detlefs, Mar 06 2010

Mathematica

Flatten[Table[5*n + {0, 1, 3, 4}, {n, 0, 20}]] (* T. D. Noe, Nov 12 2013 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 3, 4, 5}, 100] (* Harvey P. Dale, Jan 31 2022 *)

Prog

(PARI) forstep(n=0, 99, [1, 2, 1, 1], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011
(Magma) [n : n in [0..100] | n mod 5 in [0, 1, 3, 4]]; // Wesley Ivan Hurt, May 30 2016

Crossrefs

Cf. A001622, A030308, A047209, A047218.

Sequence in context: A103202 A188040 A099352 * A266728 A039132 A187970

Adjacent sequences: A047204 A047205 A047206 * A047208 A047209 A047210

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved