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A214878
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Least k such that Fibonacci(n) + Fibonacci(n+1) + ... + Fibonacci(n+k-1) is prime.
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2
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3, 2, 2, 1, 1, 1, 5, 1, 4, 2, 4, 1, 5, 1, 4, 2, 4, 1, 5, 7, 29, 2, 37, 1, 11, 163, 5, 2, 4, 1, 5, 73, 19, 1433, 4, 13, 347, 61201, 4, 47, 43, 2, 41, 1, 4, 2, 13, 1, 131, 19, 4, 5, 7, 787, 173, 31, 13, 1265, 4, 11, 53
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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Next term, if it exists, is bigger than 95000.
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LINKS
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EXAMPLE
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0+1+1=2, three summands, so a(0)=3,
1+1=2, two summands,
1+2=3, two summands,
2,
3,
5,
8+13+21+34+55=131, five summands, so a(6)=5, and so on.
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MATHEMATICA
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Table[k = n; p = Fibonacci[k]; While[! PrimeQ[p], k++; p = p + Fibonacci[k]]; k - n + 1, {n, 0, 30}] (* T. D. Noe, Jul 30 2012 *)
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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) {
BigInteger prpr=BigInteger.ZERO, prpr0;
BigInteger prev=BigInteger.ONE, prev0, curr, sum, prevSum;
long i, n;
for (n=0; ; ++n) {
prpr0 = prpr;
prev0 = prev;
sum = BigInteger.ZERO;
for (i=n; ; ++i) {
sum = sum.add(prpr);
if (sum.isProbablePrime(2)) {
if (sum.isProbablePrime(80)) break;
}
curr = prev.add(prpr);
prpr = prev;
prev = curr;
}
out.printf("%d, ", i+1-n);
prpr = prev0;
prev = prev0.add(prpr0);
}
}
}
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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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EXTENSIONS
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STATUS
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approved
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