A123136 - OEIS

%I #18 Feb 26 2024 01:56:37

%S 208,210,108,40,15,9

%N a(n+1) = ( a(n) + n*(n+1) ) / n, with a(1) = 208.

%C From a quiz. Next term is 8.5.

%H A. Frank and P. Jacqueroux, <a href="https://paulcooijmans.com/others/intcontest.pdf">International Contest</a>, 2001. Item 27.

%e a(1) = 208;

%e a(2) = (208 + 2)/1 = 210;

%e a(3) = (210 + 6)/2 = 108;

%e a(4) = (108 + 12)/3 = 40;

%e a(5) = (40 + 20)/4 = 15;

%e a(6) = (15 + 30)/5 = 9;

%e a(7) would be (9 + 42)/6 = 8.5, but that is not an integer.

%t nxt[{n_,a_}]:={n+1,(a+n(n+1))/n}; NestList[nxt,{1,208},5][[All,2]] (* _Harvey P. Dale_, Dec 04 2016 *)

%o (PARI) a=208; for(n=1,7,print1(a,","); a=(a+n*(n+1))/n)

%K nonn

%O 1,1

%A Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 30 2006