OFFSET
1,1
COMMENTS
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.
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
KEYWORD
nonn,hard,more
AUTHOR
Alex Ratushnyak, Jul 28 2012
STATUS
approved