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
Examples
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.
Crossrefs
Cf. A131183.
Programs
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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
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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
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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 *) -
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
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)