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A214874
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Starting with Fibonacci(0), the sum of a(n) successive Fibonacci numbers is prime.
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2
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3, 1, 1, 1, 5, 1, 5, 1, 5, 1, 11, 13, 131, 31, 65, 49, 47, 13, 2231, 389, 5269
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listen;
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internal format)
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OFFSET
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1,1
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COMMENTS
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Next term, 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.
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LINKS
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EXAMPLE
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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.
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PROG
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(Java)
import static java.lang.System.out;
import java.math.BigInteger;
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;
}
}
}
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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