A214094 a(0)=0, a(1)=1; a(n)=a(n-1)+a(n-2) if a(n-1)+a(n-2) is not semiprime; otherwise a(n) is the largest prime divisor of a(n-1)+a(n-2).

0, 1, 1, 2, 3, 5, 8, 13, 7, 20, 27, 47, 37, 84, 11, 19, 30, 7, 37, 44, 81, 125, 103, 228, 331, 43, 374, 139, 513, 652, 233, 885, 1118, 2003, 3121, 5124, 8245, 461, 8706, 103, 383, 486, 79, 113, 192, 61, 23, 84, 107, 191, 149, 340, 163, 503, 666, 167, 833, 1000, 1833, 2833, 2333, 5166, 7499

Offset: 0

Author

Vladimir Shevelev, Feb 16 2013

Keywords

• nonn

Comments

An analog of the Fibonacci numbers A000045 without semiprimes.

Is the sequence unbounded? (Cf. a dual sequence A214156 which is bounded.)

Links

• Peter J. C. Moses, Table of n, a(n) for n = 0..499

Crossrefs

Cf. A001358, A214156.

Programs

Maple

A214094 := proc(n)
    option remember ;
    if n <=1 then
        n;
    else
        a := procname(n-1)+procname(n-2) ;
        if numtheory[bigomega](a) =2 then
            max(op(numtheory[factorset](a)));
        else
            return a;
        end if;
    end if;
end proc: # R. J. Mathar, Feb 18 2013

Mathematica

A214094[0]:=0;
A214094[1]:=1;
A214094[n_]:=A214094[n]=If[PrimeOmega[#]==2,Last[Most[Divisors[#]]],#]&[A214094[n-1]+A214094[n-2]];
Table[A214094[n],{n,0,99}] (* Peter J. C. Moses, Feb 18 2013 *)
nxt[{a_,b_}]:={b,If[PrimeOmega[a+b]==2,FactorInteger[a+b][[-1,1]],a+b]}; NestList[nxt,{0,1},70][[All,1]] (* Harvey P. Dale, Nov 13 2017 *)