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

%I A214874 #18 Nov 22 2024 11:06:39
%S A214874 3,1,1,1,5,1,5,1,5,1,11,13,131,31,65,49,47,13,2231,389,5269,72211,
%T A214874 12587,51193
%N A214874 Starting with Fibonacci(0), the sum of a(n) successive Fibonacci numbers is prime.
%C A214874 a(22), if it exists, is bigger than 60300.
%C A214874 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 A214874 0+1+1 = 2 is prime, three summands,
%e A214874 2 is prime,
%e A214874 3 is prime,
%e A214874 5 is prime,
%e A214874 8+13+21+34+55 = 131 is prime, five summands,
%e A214874 89 is prime,
%e A214874 144+233+377+610+987 = 2351 is prime, five summands,
%e A214874 1597 is prime.
%o A214874 (Java)
%o A214874 import static java.lang.System.out;
%o A214874 import java.math.BigInteger;
%o A214874 public class A214874 {
%o A214874   public static void main (String[] args) {
%o A214874     long i, n=0;
%o A214874     BigInteger prpr = BigInteger.ZERO;
%o A214874     BigInteger prev = BigInteger.ONE, curr;
%o A214874     while (true) {
%o A214874       BigInteger bsum = BigInteger.ZERO;
%o A214874       for (i=n; ; ++i) {
%o A214874         bsum = bsum.add(prpr);
%o A214874         curr = prev.add(prpr);
%o A214874         prpr = prev;
%o A214874         prev = curr;
%o A214874         if (bsum.isProbablePrime(2)) {
%o A214874                 if (bsum.isProbablePrime(80)) break;
%o A214874                 out.printf("(%d)",i);
%o A214874         }
%o A214874       }
%o A214874       out.printf("%d, ", i+1-n);
%o A214874       n=i+1;
%o A214874     }
%o A214874   }
%o A214874 }
%Y A214874 Cf. A000040, A000045, A073684, A214878.
%K A214874 nonn,hard,more
%O A214874 1,1
%A A214874 _Alex Ratushnyak_, Jul 28 2012
%E A214874 a(22)-a(24) from _Michael S. Branicky_, Nov 21 2024