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.

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Offset: 1

Author

Pasi Airikka, Jul 01 2011

Keywords

• nonn

Examples

			a(1) = 1, a(2) = 1.
a(3) = 1 - 1 = 0, as n=3 is prime.
a(4) = 0 + 1 = 1, as n=4 is nonprime.
a(5) = 1 - 0 = 1, as n=5 is prime.
a(6) = 1 + 1 = 2, as n=6 is nonprime.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A010051, A000045.

Programs

MATLAB

a(1)=1;a(2)=1;
for i=3:n,
    true = isprime(n) ;
    if true,
       a(i)=a(i-1)-a(i-2) ;
    else
       a(i)=a(i-1)+a(i-2) ;
    end
end
% isprime returns 1 if n is prime, else 0.

Mathematica

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 *)

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

Formula

a(n) = a(n-1) + a(n-2), if n is nonprime.

a(n) = a(n-1) - a(n-2), if n is prime.

a(1) = a(2) = 1.

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