A214874 Starting with Fibonacci(0), the sum of a(n) successive Fibonacci numbers is prime.

3, 1, 1, 1, 5, 1, 5, 1, 5, 1, 11, 13, 131, 31, 65, 49, 47, 13, 2231, 389, 5269, 72211, 12587, 51193

Offset

1,1

Comments

a(22), if it exists, is bigger than 60300.

The sequence with corresponding primes begins: 2, 2, 3, 5, 131, 89, 2351, 1597, 42187, 28657, 14855327, 7763811697. The prime corresponding to a(21) = 5269 has 1729 decimal digits.

Links

Table of n, a(n) for n=1..24.

Example

0+1+1 = 2 is prime, three summands,
2 is prime,
3 is prime,
5 is prime,
8+13+21+34+55 = 131 is prime, five summands,
89 is prime,
144+233+377+610+987 = 2351 is prime, five summands,
1597 is prime.

Prog

(Java)
import static java.lang.System.out;
import java.math.BigInteger;
public class A214874 {
  public static void main (String[] args) {
    long i, n=0;
    BigInteger prpr = BigInteger.ZERO;
    BigInteger prev = BigInteger.ONE, curr;
    while (true) {
      BigInteger bsum = BigInteger.ZERO;
      for (i=n; ; ++i) {
        bsum = bsum.add(prpr);
        curr = prev.add(prpr);
        prpr = prev;
        prev = curr;
        if (bsum.isProbablePrime(2)) {
                if (bsum.isProbablePrime(80)) break;
                out.printf("(%d)", i);
        }
      }
      out.printf("%d, ", i+1-n);
      n=i+1;
    }
  }
}

Crossrefs

Cf. A000040, A000045, A073684, A214878.

Sequence in context: A322995 A336466 A052125 * A081060 A255811 A131268

Adjacent sequences: A214871 A214872 A214873 * A214875 A214876 A214877

Keyword

nonn,hard,more

Author

Alex Ratushnyak, Jul 28 2012

Extensions

a(22)-a(24) from Michael S. Branicky, Nov 21 2024

Status

approved