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A192439 a(n) = a(n-1) - a(n-2) if n is prime or a(n-1) + a(n-2) otherwise. a(1) = a(2) = 1.

%I A192439 #25 Apr 21 2024 10:01:43
%S A192439 1,1,0,1,1,2,1,3,4,7,3,10,7,17,24,41,17,58,41,99,140,239,99,338,437,
%T A192439 775,1212,1987,775,2762,1987,4749,6736,11485,18221,29706,11485,41191,
%U A192439 52676,93867,41191,135058,93867,228925,322792,551717,228925,780642,1009567
%N A192439 a(n) = a(n-1) - a(n-2) if n is prime or a(n-1) + a(n-2) otherwise. a(1) = a(2) = 1.
%H A192439 Reinhard Zumkeller, <a href="/A192439/b192439.txt">Table of n, a(n) for n = 1..1000</a>
%F A192439 a(n) = a(n-1) + a(n-2), if n is nonprime.
%F A192439 a(n) = a(n-1) - a(n-2), if n is prime.
%F A192439 a(1) = a(2) = 1.
%F A192439 a(n) >> x^n, with x = 1.28743... the largest real root of x^6 - x^5 + x^4 - x^3 + x^2 - x = 2. - _Charles R Greathouse IV_, Jul 01 2011
%e A192439 a(1) = 1, a(2) = 1.
%e A192439 a(3) = 1 - 1 = 0, as n=3 is prime.
%e A192439 a(4) = 0 + 1 = 1, as n=4 is nonprime.
%e A192439 a(5) = 1 - 0 = 1, as n=5 is prime.
%e A192439 a(6) = 1 + 1 = 2, as n=6 is nonprime.
%t A192439 nxt[{n_,a_,b_}]:={n+1,b,If[PrimeQ[n+1],b-a,b+a]}; NestList[nxt,{2,1,1},50][[All,2]] (* _Harvey P. Dale_, Dec 23 2022 *)
%o A192439 (MATLAB)
%o A192439 a(1)=1;a(2)=1;
%o A192439 for i=3:n,
%o A192439     true = isprime(n) ;
%o A192439     if true,
%o A192439        a(i)=a(i-1)-a(i-2) ;
%o A192439     else
%o A192439        a(i)=a(i-1)+a(i-2) ;
%o A192439     end
%o A192439 end
%o A192439 % isprime returns 1 if n is prime, else 0.
%o A192439 (PARI) a=vector(100);a[1]=a[2]=1;for(n=3,#a,a[n]=a[n-1]+(1-2*isprime(n))*a[n-2]); a \\ _Charles R Greathouse IV_, Jul 01 2011
%Y A192439 Cf. A010051, A000045.
%K A192439 nonn
%O A192439 1,6
%A A192439 _Pasi Airikka_, Jul 01 2011