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 A214878 Least k such that Fibonacci(n) + Fibonacci(n+1) + ... + Fibonacci(n+k-1) is prime. 2
 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)
 OFFSET 0,1 COMMENTS Next term, if it exists, is bigger than 95000. LINKS EXAMPLE 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. MATHEMATICA 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 *) PROG (Java) import static java.lang.System.out; import java.math.BigInteger; public class A214878 {   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);     }   } } CROSSREFS Cf. A000040, A000045, A214874. Sequence in context: A010269 A077450 A328330 * A086138 A170822 A054546 Adjacent sequences:  A214875 A214876 A214877 * A214879 A214880 A214881 KEYWORD nonn,hard,more AUTHOR Alex Ratushnyak, Jul 29 2012 EXTENSIONS a(37)-a(60) from T. D. Noe, Jul 30 2012 STATUS approved

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Last modified May 11 09:07 EDT 2021. Contains 343788 sequences. (Running on oeis4.)