A214874 Starting with Fibonacci(0), the sum of a(n) successive Fibonacci numbers is prime.
3, 1, 1, 1, 5, 1, 5, 1, 5, 1, 11, 13, 131, 31, 65, 49, 47, 13, 2231, 389, 5269, 72211, 12587, 51193
Offset: 1
Examples
0+1+1 = 2 is prime, three summands, 2 is prime, 3 is prime, 5 is prime, 8+13+21+34+55 = 131 is prime, five summands, 89 is prime, 144+233+377+610+987 = 2351 is prime, five summands, 1597 is prime.
Programs
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Java
import static java.lang.System.out; import java.math.BigInteger; public class A214874 { public static void main (String[] args) { long i, n=0; BigInteger prpr = BigInteger.ZERO; BigInteger prev = BigInteger.ONE, curr; while (true) { BigInteger bsum = BigInteger.ZERO; for (i=n; ; ++i) { bsum = bsum.add(prpr); curr = prev.add(prpr); prpr = prev; prev = curr; if (bsum.isProbablePrime(2)) { if (bsum.isProbablePrime(80)) break; out.printf("(%d)",i); } } out.printf("%d, ", i+1-n); n=i+1; } } }
Extensions
a(22)-a(24) from Michael S. Branicky, Nov 21 2024
Comments