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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

Table of n, a(n) for n=0..60.

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.)