A214874 - OEIS

%I #18 Nov 22 2024 11:06:39

%S 3,1,1,1,5,1,5,1,5,1,11,13,131,31,65,49,47,13,2231,389,5269,72211,

%T 12587,51193

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

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

%C 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.

%e 0+1+1 = 2 is prime, three summands,

%e 2 is prime,

%e 3 is prime,

%e 5 is prime,

%e 8+13+21+34+55 = 131 is prime, five summands,

%e 89 is prime,

%e 144+233+377+610+987 = 2351 is prime, five summands,

%e 1597 is prime.

%o (Java)

%o import static java.lang.System.out;

%o import java.math.BigInteger;

%o public class A214874 {

%o   public static void main (String[] args) {

%o     long i, n=0;

%o     BigInteger prpr = BigInteger.ZERO;

%o     BigInteger prev = BigInteger.ONE, curr;

%o     while (true) {

%o       BigInteger bsum = BigInteger.ZERO;

%o       for (i=n; ; ++i) {

%o         bsum = bsum.add(prpr);

%o         curr = prev.add(prpr);

%o         prpr = prev;

%o         prev = curr;

%o         if (bsum.isProbablePrime(2)) {

%o                 if (bsum.isProbablePrime(80)) break;

%o                 out.printf("(%d)",i);

%o         }

%o       }

%o       out.printf("%d, ", i+1-n);

%o       n=i+1;

%o     }

%o   }

%o }

%Y Cf. A000040, A000045, A073684, A214878.

%K nonn,hard,more,changed

%O 1,1

%A _Alex Ratushnyak_, Jul 28 2012

%E a(22)-a(24) from _Michael S. Branicky_, Nov 21 2024