A047208 Numbers that are congruent to {0, 4} mod 5.

0, 4, 5, 9, 10, 14, 15, 19, 20, 24, 25, 29, 30, 34, 35, 39, 40, 44, 45, 49, 50, 54, 55, 59, 60, 64, 65, 69, 70, 74, 75, 79, 80, 84, 85, 89, 90, 94, 95, 99, 100, 104, 105, 109, 110, 114, 115, 119, 120, 124, 125, 129, 130, 134, 135, 139, 140, 144, 145, 149

Offset

1,2

Comments

Also solutions to 3^x + 5^x == 2 (mod 11). - Cino Hilliard, May 18 2003

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cino Hilliard, solutions to 3^x + 5^x == 2 mod 11/, June 2003.

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

Formula

From R. J. Mathar, Jan 24 2009: (Start)

G.f.: x^2*(4+x)/((1-x)^2*(1+x)).

a(n) = a(n-2) + 5. (End)

a(n) = 5*n - 6 - a(n-1) (with a(1)=0). - Vincenzo Librandi, Nov 18 2010

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k), with b(0)=4 and b(k) = A020714(k-1) = 5*2^(k-1) for k>0. - Philippe Deléham, Oct 17 2011

a(n) = ceiling((5/3)*ceiling(3*n/2)). - Clark Kimberling, Jul 04 2012

a(n) = (5*(n-1) + 3*(n-1 mod 2))/2 = (5*(n-1) + A010674(n-1))/2. - G. C. Greubel, Nov 23 2021

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

E.g.f.: 1 + ((5*x - 7/2)*exp(x) + (3/2)*exp(-x))/2. - David Lovler, Aug 23 2022

Mathematica

{#, #+4}&/@(5*Range[0, 30])//Flatten (* Harvey P. Dale, Apr 05 2019 *)

Prog

(PARI) forstep(n=0, 200, [4, 1], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011
(Magma) [(5*(n-1) + 3*((n-1) mod 2))/2: n in [1..100]]; // G. C. Greubel, Nov 23 2021
(Sage) [(5*(n-1) +3*((n-1)%2))/2 for n in (1..100)] # G. C. Greubel, Nov 23 2021

Crossrefs

Cf. A001622, A010674, A010685 (first differences), A274406.

Sequence in context: A287962 A001983 A143575 * A177887 A032381 A191888

Adjacent sequences: A047205 A047206 A047207 * A047209 A047210 A047211

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved