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

1, 2, 3, 1, 3, 3, 6, 3, 18, 6, 24, 18, 432, 24, 456, 432, 196992, 456, 197448, 196992, 38895676416, 197448, 38895873864, 38895676416, 1512881323731695591424, 38895873864, 1512881323770591465288, 1512881323731695591424, 2288809899755012359448064967916189926490112

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Formula

a(n) = n+1 for n in {0, 1}, otherwise

a(n+1) = a(n) + a(n-1) if n mod 4 = 1,

a(n+1) = a(n) - a(n-1) if n mod 4 = 2,

a(n+1) = a(n) * a(n-1) if n mod 4 = 3,

a(n+1) = a(n) / a(n-1) if n mod 4 = 0.

From Robert Israel, Dec 22 2015: (Start)

a(4n+8) = a(4n+4)^2*(1+1/a(4n)).

a(4n+9) = a(4n+5)*(a(4n+5)+a(4n+1)+1).

a(4n+10) = a(4n+6)*(a(4n+6)-a(4n+2)+1).

a(4n+11) = a(4n+7)^2*(1+1/a(4n+3)). (End)

Example

a(0) = 1.
a(1) = 2.
a(2) = a(1) + a(0) =  2 + 1 =  3.
a(3) = a(2) - a(1) =  3 - 2 =  1.
a(4) = a(3) * a(2) =  1 * 3 =  3.
a(5) = a(4) / a(3) =  3 / 1 =  3.
a(6) = a(5) + a(4) =  3 + 3 =  6.
a(7) = a(6) - a(5) =  6 - 3 =  3.
a(8) = a(7) * a(6) =  3 * 6 = 18.
a(9) = a(8) / a(7) = 18 / 3 =  6.

Maple

f:= proc(n) option remember;
  if n mod 4 = 2 then procname(n-1)+procname(n-2)
  elif n mod 4 = 3 then procname(n-1)-procname(n-2)
  elif n mod 4 = 0 then procname(n-1)*procname(n-2)
  else procname(n-3)
  fi
end proc:
f(0):= 1: f(1):= 2:
seq(f(i), i=0..20); # Robert Israel, Dec 22 2015

Mathematica

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 *)

Prog

(BASIC)
input a(0)
input a(1)
for n=1 to 1000
begin
  if n mod 4 =1 then a(n+1):=a(n)+a(n-1)
  if n mod 4 =2 then a(n+1):=a(n)-a(n-1)
  if n mod 4 =3 then a(n+1):=a(n)*a(n-1)
  if n mod 4 =0 then a(n+1):=a(n)/a(n-1)
  print a(n+1)
end
(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

Crossrefs

Cf. A131183.

Sequence in context: A338988 A046821 A239691 * A238793 A240677 A030306

Adjacent sequences: A265493 A265494 A265495 * A265497 A265498 A265499

Keyword

nonn,easy

Author

Florent Martigne, Dec 09 2015

Status

approved