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
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.
Programs
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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); } } }
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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
Comments