A047204 Numbers that are congruent to {3, 4} mod 5.

3, 4, 8, 9, 13, 14, 18, 19, 23, 24, 28, 29, 33, 34, 38, 39, 43, 44, 48, 49, 53, 54, 58, 59, 63, 64, 68, 69, 73, 74, 78, 79, 83, 84, 88, 89, 93, 94, 98, 99, 103, 104, 108, 109, 113, 114, 118, 119, 123, 124, 128, 129, 133, 134, 138, 139, 143, 144, 148, 149

Offset

1,1

Comments

Also numbers that cannot be expressed as the sum of two 4th powers. - Cino Hilliard, Nov 23 2003

The sequence lists the indices of the multiples of 5 in A033567. - Bruno Berselli, Jan 05 2018

Links

David Lovler, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 5*n - a(n-1) - 3 for n>1, a(1)=3. - Vincenzo Librandi, Nov 18 2010

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

a(n) = floor(5*n/2) - (-1)^n. - Wesley Ivan Hurt, Sep 12 2017

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

E.g.f.: 1 + ((10*x - 1)*exp(x) - 3*exp(-x))/4. - David Lovler, Aug 23 2022

Mathematica

Select[Range[0, 200], MemberQ[{3, 4}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 12 2012 *)

Prog

(PARI) a(n)=(n-1)\2*5+4-n%2 \\ Charles R Greathouse IV, Dec 22 2011

Crossrefs

Cf. A001622, A033567.

Sequence in context: A310017 A191285 A219658 * A050035 A306901 A355477

Adjacent sequences: A047201 A047202 A047203 * A047205 A047206 A047207

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved