A216231 Fibonacci with priority for primes: a(0)=0, a(1)=1, for n >= 2, a(n) = a(n-1) + a(k), where 0 < k <= n-2 is maximal index such that a(n-1) + a(k) is prime. If there is no such k, then a(n) = a(n-1) + a(n-2).

0, 1, 1, 2, 3, 5, 7, 12, 19, 31, 43, 74, 79, 153, 227, 239, 313, 552, 631, 643, 1274, 1427, 1979, 3253, 5232, 7211, 7213, 14424, 14737, 15289, 20521, 20533, 41054, 41281, 82335, 83609, 83621, 88853, 90127, 104551, 194678, 201889, 207121, 212353, 226777, 226789

Offset: 0

Author

Vladimir Shevelev, Mar 14 2013

Keywords

• nonn

Comments

Conjecture: There exist arbitrarily long chains of consecutive prime terms.

Agrees with the lower matching number of the n-Fibonacci cube graph from n = 1 to at least n = 9. - Eric W. Weisstein, Feb 07 2025

Links

• Peter J. C. Moses, Table of n, a(n) for n = 0..9999

Crossrefs

Cf. A000045.

Programs

Maple

a:= proc(n) option remember; local k;
      if n<2 then n
    else for k from n-2 to 1 by -1
           while not isprime(a(n-1) +a(k)) do od;
         a(n-1) +a(`if`(k=0, n-2, k))
      fi
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Mar 14 2013

Mathematica

a216231[0]:=0;
a216231[1]:=1;
a216231[n_]:=a216231[n]=
Module[{k},(k=NestWhile[#-1&,n-1,(#>1)&&!PrimeQ[a216231[n-1]+a216231[#]]&];
If[k==1,k=n-2]);a216231[n-1]+a216231[k]];
Table[a216231[n],{n,0,100}] (* Peter J. C. Moses, Mar 14 2013 *)