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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A001622, A033567.

Programs

Mathematica

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

PARI

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

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