cp's OEIS Frontend

A265496 Numbers n resulting from alternately applying the operations +, -, *, / to the last term and second to last term.

%I A265496 #44 Sep 21 2023 19:25:29
%S A265496 1,2,3,1,3,3,6,3,18,6,24,18,432,24,456,432,196992,456,197448,196992,
%T A265496 38895676416,197448,38895873864,38895676416,1512881323731695591424,
%U A265496 38895873864,1512881323770591465288,1512881323731695591424,2288809899755012359448064967916189926490112
%N A265496 Numbers n resulting from alternately applying the operations +, -, *, / to the last term and second to last term.
%F A265496 a(n) = n+1 for n in {0, 1}, otherwise
%F A265496   a(n+1) = a(n) + a(n-1) if n mod 4 = 1,
%F A265496   a(n+1) = a(n) - a(n-1) if n mod 4 = 2,
%F A265496   a(n+1) = a(n) * a(n-1) if n mod 4 = 3,
%F A265496   a(n+1) = a(n) / a(n-1) if n mod 4 = 0.
%F A265496 From _Robert Israel_, Dec 22 2015: (Start)
%F A265496 a(4n+8)  = a(4n+4)^2*(1+1/a(4n)).
%F A265496 a(4n+9)  = a(4n+5)*(a(4n+5)+a(4n+1)+1).
%F A265496 a(4n+10) = a(4n+6)*(a(4n+6)-a(4n+2)+1).
%F A265496 a(4n+11) = a(4n+7)^2*(1+1/a(4n+3)). (End)
%e A265496 a(0) = 1.
%e A265496 a(1) = 2.
%e A265496 a(2) = a(1) + a(0) =  2 + 1 =  3.
%e A265496 a(3) = a(2) - a(1) =  3 - 2 =  1.
%e A265496 a(4) = a(3) * a(2) =  1 * 3 =  3.
%e A265496 a(5) = a(4) / a(3) =  3 / 1 =  3.
%e A265496 a(6) = a(5) + a(4) =  3 + 3 =  6.
%e A265496 a(7) = a(6) - a(5) =  6 - 3 =  3.
%e A265496 a(8) = a(7) * a(6) =  3 * 6 = 18.
%e A265496 a(9) = a(8) / a(7) = 18 / 3 =  6.
%p A265496 f:= proc(n) option remember;
%p A265496   if n mod 4 = 2 then procname(n-1)+procname(n-2)
%p A265496   elif n mod 4 = 3 then procname(n-1)-procname(n-2)
%p A265496   elif n mod 4 = 0 then procname(n-1)*procname(n-2)
%p A265496   else procname(n-3)
%p A265496   fi
%p A265496 end proc:
%p A265496 f(0):= 1: f(1):= 2:
%p A265496 seq(f(i),i=0..20); # _Robert Israel_, Dec 22 2015
%t A265496 a[0] = 1; a[1] = 2; a[x_] := a[x] = Which[Mod[x, 4] == 2, a[x - 1] + a[x - 2], Mod[x, 4] == 3, a[x - 1] - a[x - 2], Mod[x, 4] == 0, a[x - 1] a[x - 2], Mod[x, 4] == 1, a[x - 1]/a[x - 2]]; Table[a@ n, {n, 0, 30}] (* _Michael De Vlieger_, Dec 22 2015 *)
%o A265496 (BASIC)
%o A265496 input a(0)
%o A265496 input a(1)
%o A265496 for n=1 to 1000
%o A265496 begin
%o A265496   if n mod 4 =1 then a(n+1):=a(n)+a(n-1)
%o A265496   if n mod 4 =2 then a(n+1):=a(n)-a(n-1)
%o A265496   if n mod 4 =3 then a(n+1):=a(n)*a(n-1)
%o A265496   if n mod 4 =0 then a(n+1):=a(n)/a(n-1)
%o A265496   print a(n+1)
%o A265496 end
%o A265496 (PARI) lista(nn) = {print1(x = 1, ", "); print1(y = 2, ", "); for (n=1, nn, if (n % 4 == 1, z = x+y); if (n % 4 == 2, z = y-x); if (n % 4 == 3, z = x*y); if (n % 4 == 0, z = y/x); print1(z, ", "); x = y; y = z;);} \\ _Michel Marcus_, Dec 22 2015
%Y A265496 Cf. A131183.
%K A265496 nonn,easy
%O A265496 0,2
%A A265496 _Florent Martigne_, Dec 09 2015