A047204 - OEIS

%I #46 Aug 24 2022 09:00:42

%S 3,4,8,9,13,14,18,19,23,24,28,29,33,34,38,39,43,44,48,49,53,54,58,59,

%T 63,64,68,69,73,74,78,79,83,84,88,89,93,94,98,99,103,104,108,109,113,

%U 114,118,119,123,124,128,129,133,134,138,139,143,144,148,149

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

%C Also numbers that cannot be expressed as the sum of two 4th powers. - _Cino Hilliard_, Nov 23 2003

%C The sequence lists the indices of the multiples of 5 in A033567. - _Bruno Berselli_, Jan 05 2018

%H David Lovler, <a href="/A047204/b047204.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F a(n) = 5*n - a(n-1) - 3 for n>1, a(1)=3. - _Vincenzo Librandi_, Nov 18 2010

%F G.f.: x*(3 + x + x^2) / ((1 + x)*(x - 1)^2). - _R. J. Mathar_, Oct 08 2011

%F a(n) = floor(5*n/2) - (-1)^n. - _Wesley Ivan Hurt_, Sep 12 2017

%F 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

%F E.g.f.: 1 + ((10*x - 1)*exp(x) - 3*exp(-x))/4. - _David Lovler_, Aug 23 2022

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

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

%Y Cf. A001622, A033567.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_