A214878 Least k such that Fibonacci(n) + Fibonacci(n+1) + ... + Fibonacci(n+k-1) is prime.

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

Offset: 0

Author

Alex Ratushnyak, Jul 29 2012

Keywords

• nonn
• hard
• more

Comments

Next term, if it exists, is bigger than 95000.

Examples

			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.
		

Crossrefs

Cf. A000040, A000045, A214874.

Programs

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);
    }
  }
}

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 *)

Extensions

a(37)-a(60) from T. D. Noe, Jul 30 2012