%I #19 Aug 26 2012 11:27:14
%S 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,
%T 73,19,1433,4,13,347,61201,4,47,43,2,41,1,4,2,13,1,131,19,4,5,7,787,
%U 173,31,13,1265,4,11,53
%N Least k such that Fibonacci(n) + Fibonacci(n+1) + ... + Fibonacci(n+k-1) is prime.
%C Next term, if it exists, is bigger than 95000.
%e 0+1+1=2, three summands, so a(0)=3,
%e 1+1=2, two summands,
%e 1+2=3, two summands,
%e 2,
%e 3,
%e 5,
%e 8+13+21+34+55=131, five summands, so a(6)=5, and so on.
%t 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 *)
%o (Java)
%o import static java.lang.System.out;
%o import java.math.BigInteger;
%o public class A214878 {
%o public static void main (String[] args) {
%o BigInteger prpr=BigInteger.ZERO, prpr0;
%o BigInteger prev=BigInteger.ONE, prev0, curr, sum, prevSum;
%o long i, n;
%o for (n=0; ; ++n) {
%o prpr0 = prpr;
%o prev0 = prev;
%o sum = BigInteger.ZERO;
%o for (i=n; ; ++i) {
%o sum = sum.add(prpr);
%o if (sum.isProbablePrime(2)) {
%o if (sum.isProbablePrime(80)) break;
%o }
%o curr = prev.add(prpr);
%o prpr = prev;
%o prev = curr;
%o }
%o out.printf("%d, ", i+1-n);
%o prpr = prev0;
%o prev = prev0.add(prpr0);
%o }
%o }
%o }
%Y Cf. A000040, A000045, A214874.
%K nonn,hard,more
%O 0,1
%A _Alex Ratushnyak_, Jul 29 2012
%E a(37)-a(60) from _T. D. Noe_, Jul 30 2012